This page gives hints for how to edit nLab-pages.
If you feel you can most easily start by modifying an example, look at the template page and do experiments in the Sandbox.
Hit “edit page” to see how pages are coded. Use the Sandbox to warm up. The key point is that links to other pages are placed in [[double brackets]].
There is no feature to preview your edits. Instead, submit them and then edit again. Two successive submissions with the same signature and made within 30 minutes of each other count as one.
To create a new page on the Lab first make an existing page request a link to it, and then click on that requested link.
In detail:
Create a link request.
Identify any existing Lab page which should eventually refer to your new page.
(At least one such page ought to exist, if your new page is related to anything, but if you just cannot think of any, use the Sandbox page).
Hit “edit” on that existing page.
In the resulting edit pane, add the string
[[your new page name]]
at some sensible point in the source code.
(By default: in the “Related entries”-section.)
Hit “submit” below the edit pane.
See the existing page render again, now with your edit included. If your new page name did not exist yet as a page, you will see that string appear, in the existing entry, in gray with a clickable question mark behind it.
Satisfy the link request.
Click on that question mark to open the edit pane for the new page.
Edit.
Once you hit “Submit” below that edit pane, the new page will appear.
There is no preview mechanism: Just keep cycling through “Submit” and “Edit” until you are satisfied.
Watch out: the name of a page is case sensitive, so make your link lowercase if it comes at the beginning of a sentence. ([[like this|Like this]].) We loosely agreed to try to follow that and some other naming conventions; see below.
Use redirects to allow for other casing to be used when linking to the page elsewhere in the nLab.
When you edit a page, you should put your name (with normal capitalisation and spacing) in the box after ‘Submit as’. If you don’t, then your contribution will be credited to ‘Anonymous’ (formerly the AnonymousCoward).
Once you edit a page for the first time, your name will appear at the bottom, grayed out with a question mark since there is no page with your name yet. You may take this as an invitation to create a user page and tell us about yourself. But if you don’t want to or don’t have the time right now, you can forget about this. If you just want to show up on category: people, then you make a page containing only ‘category: people’ (or someone else may do this for you).
To create your user page, simply click the question mark that appears next to your name at the bottom of the page after making a modification and add content to the edit box that appears. If you’d like to make a user page prior to modifying an existing page, you can do so by making some trivial modification to the Sandbox, which will put your name at the bottom of the page where you can click the question mark. (Or hack the URL.)
The following naming conventions for new entries are not set in stone, but we're following them for now. Changing page titles results in unnecessary work for the lab elves?, so you should try to follow these if possible (or dispute them if not). It is most important to follow these in links to pages that don't yet exist, so that the pages will be created at the correct title (and only once).
Page titles should contain only ASCII characters.
[[omega-category]] instead of [[$\omega$-category]] or [[∞-category]].$\omega$-[[omega-category|category]]. To produce ‘∞-category’, try [[omega-category|∞-category]]. (The former has proper math-mode formatting, while the latter has proper link scope.) Unfortunately, [[omega-category|$\omega$-category]] does not work. You can also use redirects? to make [[∞-category]] produce ‘∞-category’, but only when the page already exists.Page titles should be singular nouns.
Examples: Use [[category]] instead of [[categories]], [[faithful functor]] instead of [[faithful]], and [[categorification]] instead of [[categorify]] or [[categorified]].
Tricks: To produce ‘categories’, try [[category|categories]]. To produce ‘faithful endofunctor’, try [[faithful functor|faithful]] [[endofunctor]] . Again, you can use redirects to make [[categories]] produce ‘categories’, if the page already exists.
Reason: We want only one page on a given concept, regardless of variations in grammar.
Exception: Recently we have started to have page titles that are complete sentences (without capitalization or punctuation) that state a simple theorem (typically a universal affirmation in the Aristotelian sense) such as compact Hausdorff rings are profinite or derivations of smooth functions are vector fields.
Page titles should be uncapitalized, except for words that are always capitalized.
Examples: Use [[homotopy theory]] instead of [[Homotopy Theory]], but use [[Lie algebra]].
Tricks: To produce ‘Homotopy theory is important!’, try [[homotopy theory|Homotopy theory]] is important!. If you do this a lot, then you can again create a redirect, if the page exists.
Reason: We want only one page on a given concept, regardless of variations in grammar.
Except as contradicted above, use standard American English spelling conventions.
Examples: Use [[center]] instead of [[centre]] and hyphens as shown in the ASCII-only requirement.
Tricks: To produce ‘centre’, try [[center|centre]]. Or, again, make a redirect.
Reason: Much of this is written by Urs Schreiber, who uses American English spelling (for the most part, at least).
Regardless of the above, pages named after specific categories should use the capitalised singular abbreviated form.
Examples: Use [[Set]] instead [[Sets]] and [[Cat]] instead of [[Category]].
Tricks: Although things like ‘’ work best in math mode and even ‘’ alone looks most consistent that way (with proper math-mode formatting), you have to make the link ‘Set’ outside of math mode.
It happens at times that you may wish the material in existing pages A and B, would be merged into a single page. (This occurs notably after any user accidentally created a new page unaware that another page on the topic was already in existence.)
In most cases it will be best to raise the issue on the nForum, check if regulars agree that the pages ought to be merged, and hope that one of them takes care of it.
If you do decide to merge on your own, here are instructions.
The basic idea is evident: Merge the content, delete one of the entries and make its previous name redirect to the remaining page. But the redirecting takes some care; and a complication is that Lab pages cannot be deleted (not by regular users, anyway) but only “orphaned”.
Suppose that A is the name of the page to be kept and and that B is the name of the one to be deleted. Then:
Edit A
so that it looks like the intended merged entry.
Add the line “[[!redirects B]]” to the bottom.
And in case the page B itself has [[!redirects X]]-lines in its source, copy them all over to A.
Submit.
Edit B
by first clearing its content (e.g. with a keystroke such as Ctrl-A Del).
Click the checkbox ‘Change page name.’, which will bring up a new field ‘New name:’.
In that field, append “> history” to the string “B”, so that the new page name becomes “B > history”.
(The idea is to change to any name that is neither coincides with an existing nor with a future entry.)
Do not submit the edit yet.
Before finishing we need to work around what the wiki software thinks is intended behaviour:
Click in the big edit box – this will automatically add the line “[[!redirects B]]”.
(The wiki software is trying to be helpful, not knowing that we want to delete the entry for good.)
Delete that line (to ensure that all requests for B will now take the reader to A),
and instead add “see [[A]]”.
(This just in case anyone ever comes across this page in the future – which should not actually happen, due to the [[!redirects B]]-command meanwhile added to
A.)
Finally ready to submit this quasi-deletion of B.
But since the page’s name was changed in the process, the software will require announcing this edit in the box below the edit box. So enter there something like:
“As we discussed, I am orphaning this page and have merged its previous content into page "A".”
Submit.
Please make a request at the nForum.
There are numerous ways you can help out and get acquainted with the community even if you don’t (yet) feel comfortable writing math publicly on a wiki.
You can correct typos and spelling errors, fix links, create links, create redirects (there are many pages that still need redirects created for alternate and plural forms of the title), organize pages, and so on.
You can ask questions (see previous question), and join discussions, at the nForum, and comment at the nCafe.
You can try writing small additions to existing pages, for instance a paragraph or two that helps explain something that puzzled you initially. If you aren’t entirely positive that what you wrote was correct, when you announce your edit at Latest Changes on the nForum, you can mention that you’re unsure and someone will usually reassure you or give a correction.
You should, of course, include a link or URL to the page or pages that you wish to cite. You should also give the information about which version of the page you are citing, since pages change over time. The version number can be found as follows: look at the bottom of the page where it says “Back in time ( revisions)”; the current version number is .
You can link directly to the version you want to cite by using a url such as
http://ncatlab.org/nlab/revision/PageName/VERSIONNUMBERWe recommend that if you only include one URL, it be of the form show/PageName which will point to whatever version of the page is current when it is accessed. This is because pages generally improve over time, and whoever is following your reference ought to be taken to the best, up-to-date version of the page. Anyone who cares about finding the exact version of the page that you cited can figure out how to find it in the history.
On the other hand, if you can give two URLs (this would be cumbersome in a printed paper, but is possible with links on a web page), then it may be helpful to give the appropriate revision link as well as the show one.
All nLab pages now include a “Cite” link at the bottom of the page which produces a BibTeX entry in accord with the suggestions above.
We encourage authors to structure pages by sections and subsections as indicated in the
Every page starts out tiny and may not seem to need a structure by subsections. But it will grow and eventually the information it provides may be hard to recognize without some global structure guiding the reader’s attention. After all, the natural evolution of articles makes the Lab function more like an encyclopedia than a novel. Moreover, even with little material there in the beginning, a structure by subsections helps the collaborative process, as it makes it easer to decide for new authors where to add what.
You should include actual mathematics in appropriate environments, as familiar from textbooks and research articles in mathematics.
As of mid-2018, one can use environments exactly as in LaTeX.
For example the code
produces:
Theorem
Some theorem.
The available environments are listed below. Some environments can be specified in several ways.
| Environment | Syntax |
|---|---|
| Definition | definition |
| defn | |
| Theorem | theorem |
| thm | |
| Proof | proof |
| Proposition | proposition |
| prop | |
| prpn | |
| Remark | remark |
| rmk | |
| Corollary | corollary |
| cor | |
| Lemma | lemma |
| lem | |
| Notation | notation |
| notn | |
| Terminology | terminology |
| Conjecture | conjecture |
| conj | |
| Scholium | scholium |
| Assumption | assumption |
| assum | |
| Example | example |
| Exercise | exercise |
| Statement | statement |
Labels for the purpose of referencing work exactly as in LaTeX: put \label{SomeTheorem} anywhere inside the environment block. Later, one can reference it as Theorem . Again, see the source of this page for how to produce this reference.
Any character but closing brace is allowed in labels here (note that this is different from equation labels below).
An older syntax for this is described at Instiki theorem environments:
A definition should be enclosed in
+-- {: .num_defn}
###### Definition
(Definition goes here)
=--A proposition or theorem should be enclosed in
+-- {: .num_prop}
###### Proposition
(Proposition goes here)
=--or
+-- {: .num_theorem}
###### Theorem
(Theorem goes here)
=--and their proof in
+-- {: .proof}
###### Proof
(Proof goes here.)
=--A corollary in
+-- {: .num_cor}
###### Corollary
(Corollary goes here)
=--and a remark in
+-- {: .num_remark}
###### Remark
(Remark goes here)
=--Beware:
Contrary to the behaviour with the LaTeX syntax described above, you do need to use the labels exactly as given above. That is, it needs to be defn, thm, and cor; neither definition nor theorem nor corollary (nor other abbreviations such as def) will be recognized by the software.
There must be a whitespace after the closing =--. Otherwise the parser will not recognize the end of the environment and will in fact ignore its content and all following code (unless and until it happens to spot an unpaired =-- further down the line).
Hence best to instead use the above LaTeX syntax, where possible.
A central point of the Lab is that information is linked. Little value is added to the world when information is added to an Lab page if it is not interlinked there with other Lab entries such as to make sure that users who might look for it will actually eventually find it by following some links.
Therefore you should hyperlink the central keywords in what you write, by enclosing them in square brackets. Ideally, each and every keyword would be hyperlinked, certainly when it occurs first. Don’t assume that the reader has the same background as you have. If you explain something by invoking other technical terms, at least provide links to Lab entries where these other terms are defined.
Analogously, when you create a new page, make sure that it is linked to from at least one relevant other page. An entry on a new kind of manifold deserves to be linked to from a list of “related entries” at manifold, for instance.
Apart from guiding users to your entry this way, notably this will also help search engines to index the Lab and make your new entry appear listed when people search for something related.
There is really no such thing as a “global convention on the Lab” for ambiguous meaning of mathematical terms and symbols. Unlike in a text book by a single or a handful of authors, there is just no way that we can even try to enforce global conventions. Typically each author decides on his or her own.
Therefore the general rule is: whatever you write in some entry, try to make sure that you provide enough context that the relevant conventions are clear. If you find yourself using some notation for the first time on a page and are worrying if readers will read it as intended, be sure to add a parenthetical remark (where we use here the convention that…) or similar.
If you feel that you need to refer to a specific convention repeatedly over several Lab pages, just create another page that states the convention, and then simply point to that page.
One example of this that we have is the implicit infinity-category theory convention-page.
The nLab uses the itex2MML software with custom in-house hacks to typeset formulas. Its syntax is based on TeX (supporting many macros from plain TeX and LaTeX), with some important unfortunate differences documented below. The reasons for these differences are mostly historical: when the nLab was created in 2008, there was no standardized software to support formulas (like MathJax these days), with multiple competing solutions like itex2MML, jsMath, and others.
One of the notable ways in which iTeX differs from LaTeX is that in iTeX’s math mode, a string of letters without spaces in between is interpreted as a single identifier. This has the advantage that you can invent new identifiers without needing to use \operatorname or \DeclareMathOperator, but it means that when you don’t want a string of letters interpreted that way you need to put spaces in between. For example, $sin(x)$ produces which is probably what you want, but $h=gf$ produces , whereas you probably wanted to write $h=g f$ to get . On the other hand, you can (and, for the sake of the LaTeX output, probably should) use $\sin(x)$, etc.
iTeX is not LaTeX. Their similarity can make the differences all the more jarring. Here is a list of the differences that we know about together with suggested work-arounds.
Numbers are one thing. The syntax $10^10$ produces in iTeX but in LaTeX. The safe syntax is to always use braces: $10^{10}$ is consistent.
Numbers include punctuation. Periods and commas within numbers are numbers. This is so that $1,000,000.00$ (or $1.000.000,00$ if you are European) renders correctly as and not . When combined with the previous difference, this means that $t^3.2$ renders as instead of . Either use braces or spaces. (However, for some reason, $t^3,2$ renders as like you'd expect from TeX, so the two differences don't interact entirely logically. This might have been different in earlier versions of iTeX.)
Operator names. Since iTeX does not have macro support, extending the list of operator names would be difficult except for the fact that neighbouring strings of letters get combined into an operator name. Thus $cos$ produces . However, in LaTeX this produces . Where the operator name is a standard LaTeX one, such as \cos, the backslash can be added so $\cos$ renders correctly in both cases. Where the operator name is not a standard LaTeX one, say Poly, the safe syntax is to use \operatorname; thus $\operatorname{Poly}$ renders correctly as in both situations. If you don't want an operator name, then use spaces; thus $c o s$ produces .
Whitespace in embedded text. In LaTeX $x \text{ and } y$ renders as but in iTeX it renders as . This is because MathML says that fore and aft whitespace on mtext elements should be swallowed. The safe syntax is $x\;\text{and}\;y$.
Two-character relations. In LaTeX, two neighbouring relation symbols are combined into one relation symbol. Thus $y := f(x)$ becomes , while $y = -f(x)$ becomes because a minus sign is a unary operator instead of a binary relation. Since MathML doesn't know the difference between unary operators and binary relations, it is inconvenient for iTeX to do this, so $y := f(x)$ comes out as instead. The safe syntax is $y \mathrel{:=} f(x)$, which produces . However, in many cases, there is a combined command that you can use. In this case, $y \coloneqq f(x)$ produces . This method is better when available; even in LaTeX, it will adjust the vertical positioning a bit to look nice.
Non-ascii characters. iTeX is designed only to parse the mathematical sections of any page and so it assumes that any strange characters will be generated via iTeX commands such as \infty instead of being directly input as ?. iTeX actually takes an extreme view on this and will not parse mathematics if it includes non-ascii characters. In ordinary mathematics this should not be a problem since one should use the iTeX commands themselves to produce such characters. Where it can be a problem is in \text commands embedded in mathematics because these are still parsed by iTeX even though it does nothing with them. Thus \text{?} is not a legal construct and will simply produce . Since iTeX does not allow nesting, the construction \text{$\infty$} will not work. There are two possibilities:
\text command: \text{in~}\infty{-categories} produces (note the forced space, simple whitespace there will not work).\text{in ∞-categories produces . Named entities will not work here as they get converted to unicode internally before being sent to the iTeX parser.The characters < and > are interpreted as beginning or ending HTML tags. To make a less-than or greater-than sign in iTeX math mode, use \lt and \gt respectively. For example, $0\lt 1$ produces .
You can use HTML/XML/SGML character entity references. If the character you want has a mnemonic HTML name, like é for é, you can use that. Otherwise, you can use an SGML numerical code, like 㒫 for 㒫, that corresponds directly to Unicode. To look up the numbers for SGML characters, try the Unicode Character Names Index. Toby has a complete list of HTML and XML character entity references (or try the Unicode Databank pages listed below) with individual pages where you can check browser compliance (originally for when you couldn't take even things like ↔ for granted, but even now ‎ and   may be lacking). While you can use this technique for mathematical symbols too, it's best to do those in iTeX as explained above.
When you create a section header, you can add an HTML anchor tag to it with the following syntax:
## Heading {#anchorname}Note that the tag must be placed at the end. Then you can make a link to it using the syntax:
[[some page#anchorname|link text]]If the link is to the same page then the page name can be omitted by using the syntax:
[link text](#anchorname)Note that a single bracket link with only an anchor doesn’t function correctly when viewing a particular revision or a difference between revisions.
Strangely single bracket link texts allow math expressions while double bracket texts don’t. For example
[$Set^\to$](Sierpinski+topos) vs [[Sierpinski topos|$Set^\to$]] vs [$Set^\to$](https://ncatlab.org/nlab/show/Sierpinski+topos).produces
Of course, you can link to it from outside the nLab by adding http://ncatlab.org at the beginning of the link.
Note that if you skip the first step, it is still possible to create a link to a subsection, since (at least if the page has a table of contents) every section on the page is automatically assigned an HTML anchor by Instiki. However, using such links is not encouraged, since the automatically generated anchor names will change whenever the page is rearranged and go away if a manual anchor name is added, which will cause such links to break.
The same type of syntax enables one to link to arbitrary text blocks such as paragraphs or list elements, such as a link to this paragraph itself. Note that these tags must be at the start of the text. In particular, a bibliographic reference can be made by first by creating an anchor:
* {#xyz} Reference which can then be linked to from within the same page by writing
[link text](#xyz). When you write a numbered definition or proposition or theorem, you can also simultaneously create an anchor.
In the LaTeX-style syntax, use \label inside the theorem/etc. environment as usual.
In the older syntax, write:
+-- {: .num_defn #definitionname}
###### Definition
...
=--
+-- {: .num_prop #propname}
###### Proposition
...
=--
+-- {: .num_theorem #theoremname}
###### Theorem
...
=--Then you can link to it in the same ways:
[[some page#theoremname|see this theorem]]
[see this theorem](#theoremname)When you link to a theorem on the same page, however, it’s better to use the \ref syntax (without the space between \ref and {, it is present here just to avoid it being parsed):
see Theorem \ref {theoremname}This inserts the number as well as creating a hyperlink, and will also work properly when the page is exported to LaTeX.
To make an equation be automatically numbered use angular brackets instead of dollar signs
\[
\exp(\pi i) + 1 = 0
\]To refer to this numbered equation, add a label
\[
\label{SomeEquation}
\exp(\pi i) + 1 = 0
\]and then refer to it later in the text by using \eqref just like in LaTeX:
See equation \eqref {SomeEquation}.(Leave out the space after \eqref, which is present here just to avoid it being parsed.)
There is also an older, non-TeX syntax for equation references (use an actual colon : in place of -colon-, which is used here to prevent the example from being parsed):
See equation (eq-colon-SomeEquation). Only word characters are allowed in LaTeX display labels. In particular, the hyphen character - cannot be used. This is in contrast to labels for theorem environments. This is due to use of different parsers. Instead of \label{foo-bar}, consider \label{FooBar}.
Since 2019, the recommended way to make a table of contents for a page (and almost any page should have a table of contents) is to write the following at the top of the page, or wherever the table of contents is to appear, without the space between the backslash and tableofcontents.
\ tableofcontentsAn older method is to write
* table of contents
{: toc}
(including the line break!) at the position where the table of contents is to appear. You may want to label the table of contents by writing
# Contents #
* table of contents
{: toc}or (at the top of the page)
# [page title] #
* table of contents
{: toc}(which also gives the opportunity to use a more nicely formatted page title if special characters or mathematical formatting are wanted).
The items in the table of contents will be the section headlines marked by
## top level headline ##
### second level headline ###
etc.Instead of “table of contents” after the asterisk, you can write anything you like: this line will not be displayed but is still required to kick in the CSS that makes this possible.
It is important that the section headings not contain anything that shouldn’t go in the table of contents. Whilst formatting is allowed, wiki-links are not (since then the entry in the table of contents would have a link inside of a link).
At the end of each Lab entry should be a section
## Referencesor sometimes
## Literaturewhich contains a bullet list of relevant references. A standard way to format an entry is this list is the following:
* {#LastnameAnotherlastnameYear} [[Firstname Lastname]], [[Anotherfirstname Anotherlastname]], _Title_, Journal **volume** issue (year) firstpage-lastpage [[arXiv:xxxx.yyyyy](https://arxiv.org/abs/xxxx.yyyyy), [doi:xyz](http://doi.xyz)]which comes out as
- Firstname Lastname, Anotherfirstname Anotherlastname, Title, Journal volume issue (year) firstpage-lastpage [arXiv:xxxx.yyyyy, doi:xyz]
Given such an item in the list of references, a standard way to reference it from the main text of the entry is as follows:
see ([Lastname & Anotherlastname Year, theorem 1.3](#LastnameAnotherlastnameYear))which comes out at
This produces a hyperlink, and in fact such that following it brings up the above bullet item highlighted by a gray box.
In general, the place to make comments and ask questions is at the nForum. Each page has a ‘Discuss this page’ link in the menu at the top. Clicking on this will take to the thread for discussion of the page in the ‘Latest changes’ category, if it already exists. Just add a comment to the thread. If it does not exist, you will be taken to the nForum home page. Just start a new discussion there, selecting ‘Latest changes’ as the category and with title the same as the nLab page, and make your comment/ask your question.
Whilst questions are answered and discussions are carried out at the nForum, the conclusion should often be recorded on an nLab page. If it’s about a particular page, then of course put it on that page; if it’s a general question then it could be recorded on this How To or the FAQ?. As this is a wiki, you can do this recording yourself when your question is answered.
That said, the wiki software does contain a mechanism for putting questions and comments on a wiki page itself: edit the page and put your comment or question in a query block as shown in this example:
+-- {: .query}
How do I ask a question?
=--which produces
How do I ask a question?
In general, this is the wrong way to go about asking a question. When you put a query box on a page, often none of the other contributors will notice it for a long time, so it will take a long time for the question to be answered, and in the meantime it makes the page cluttered and ugly for other readers. However, occasionally it may be appropriate to record a brief question in a query box, if it has already been discussed at the nForum and the conclusion was not satisfactory. In this case a link to the nForum discussion should be included in the query box in preference to any lengthy detail about the question and discussion.
(Before the nForum existed, it was much more common to ask questions using query boxes. Some such query boxes still remain undiscovered on various pages, but whenever we find one we generally migrate it to the n-Forum.)
If you want to make some text stand out (an important theorem, or slogan), you can do it using a standout box. The mechanism is similar to a query box, although the purpose is different: while a query box is for a temporary question and should be removed once that question is resolved, a standout box is a permanent feature of a page that simply emphasizes a small amount of text. To make a standout box, write:
+-- {: .standout}
First quantization is a mystery, but second quantization is a functor.
=--which produces
First quantization is a mystery, but second quantization is a functor.
If you have some material at a page called foo that you want to include directly in pages called bar and baz, then type
[[!include foo]] in bar and baz. For an example, see how contents is included at the tope of this page. Also see how contents itself has been formatted so that it will appear as a sidebar when included.
Besides such sidebars that appear in many pages, you can also use inclusion to put in something that contains a bunch of ugly code (such as raw SVG, see here) without mucking up the rest of the page. That is, you put your messy code in bar/foo and then put
[[!include bar/foo]] in bar. Note that this is for something that, logically, should appear within bar itself, which is why bar appears in the name of the included page.
Note that the included page goes directly in where it is called with no surrounding whitespace. This can mean that formatting rules are broken on the include. For example, if the included file starts and ends with a div tag and is included with no surrounding blank lines then this breaks the rules and will generate an error.
To upload a file, proceed as follows:
Type
[FileName](/nlab/files/filename.xyz)
into the edit page for some entry;
hit “submit”;
in the rendered entry, find a grayish link labeled “FileName”;
click on the link to open an upload dialogue and follow the instructions there;
notice that the dialogue field “Description” is asking for the text that will appear hyperlinked to your file. If you put no text here, no link to your file will appear by itself;
complete the dialogue by hitting “upload”.
After this, the file is now sitting at this URL:
https://ncatlab.org/nlab/files/FileName.xyz Alternatively,
Type
[[FileName.xyz:file]]
into the edit page for some entry, or
[[FileName.xyz:pic]]
in the case of a picture;
hit “submit”;
in the rendered entry, find a grayish link labeled “FileName.xyz” followed by a question mark;
click on the question mark to open an upload dialogue and follow the instructions there;
notice that the dialogue field “Description” is asking for the text that will appear hyperlinked to your file. If you put no text here, no link to your file will appear by itself;
complete the dialogue by hitting “upload”;
find in the rendered entry the previously grayish text “FileName.xyz” replaced by the text that you entered into the “Description”-box in the file upload dialogue, and hyperlinked to your file;
due to a bug, if you want that link to persist, you need to make any further edit to the entry (e.g. add a whitespace) and “submit” again.
After this, the file is now sitting at this URL:
https://ncatlab.org/nlab/files/FileName.xyz Hints:
If you uploaded a picture using the :pic syntax and do not wish to tweak the displayed image in any way, there is no need to do anything. If you uploaded it using the :file syntax, you will probably want to remove the file upload code
[[FileName.xyz:file]](which renders to a link to the file) and instead add a line like
<img src="/nlab/files/FileName.xyz"/>which makes the actual image show up in entry, There are a number of other posible parameters for an imagefromfile block, see .
If you uploaded a pdf (or similar) for a reference, you will probably want to make sure that the “Description” text in the upload dialogue is “pdf” (or similar), so that the code
A. Name, _A title_, A Journal, AYear (<a class='existingWikiWord' href='/nlab/files/FileName.xyz' title='HoTT proposal 2009'>HoTT proposal 2009</a>)renders to
“A. Name, A title, A Journal, AYear (pdf)”
with “pdf” hyperlinked to your file.
There is a size limit for files to upload. The functionality is meant to be used for uploading ingredients of Lab entries (such as pictures or references) which are not available for linking elsewhere on the web, or not reliably so.
If you try to abuse the file upload for archiving your personal files, the steering committee will intervene.
To redirect the plural
[[categories]]to the existing page
[[category]]simply edit category and insert
[[!redirects categories]]at the bottom of the page. From then on, whenever you link to categories, you are taken to category. This saves you the headache of typing things like
[[category|categories]]For example, if you open category for editing and look at the bottom, you will find
[[!redirects categories]]
[[!redirects Category]]
[[!redirects Categories]]Therefore, categories, Category, and Categories all redirect to category now.
Redirects only work if the desired redirected page [[categories]] does not already exist.
Don’t worry, this is a feature, not a bug, designed to avoid silly things like infinite redirect loops, etc.
In the event that [[categories]] does exist already, then it probably should not if [[category]] already exists.
If you run into this situation, you can help by transferring material from [[existing pages]] to [[existing page]] and change the name of [[existing pages]] to [[existing pages > history]]. Now the redirects will work and we maintain the history of any revisions that were made to [[existing pages]].
Currently, there are many pages with titles that would ideally include symbols, e.g. (infinity,1)-category.
Prior to redirects, if you wanted to link to this page, you could either write the ugly version
[[(infinity,1)-category]]or worse, if you were using the plural version you could write
[[(infinity,1)-category|(infinity,1)-categories]]Alternatively, you could get a little fancy with
$(\infty,1)$-[[(infinity,1)-category|(infinity,1)-categories]]which preserves the distinction between math and text but doesn’t allow the link to cover the entire linking phrase.
Currently, if you open (infinity,1)-category for editing and look at the bottom, you will see
[[!redirects (∞,1)-category]]
[[!redirects (∞,1)-categories]]
[[!redirects (infinity,1)-categories]]This means that we can now simply insert links like (∞,1)-categories and be redirected to (infinity,1)-category. The only downside here (compared to the previous alternative) is that math material is in the text font. (Some of us even write $2$-[[2-category|category]] for this reason.)
The ∞ symbol included in the link is not obtained via the itex syntax $\infty$. To actually include non-ASCII symbols in links, you either need to be an expert at unicode or simply find the ‘∞’ symbol already displayed somewhere, copy it, and paste the symbol into the edit box. To see what I mean, you can edit this page to look at the source code for the link: (∞,1)-categories.
Occasionally you may come across a situation where a redirect exists for a link that you’d like to create a separate entry for. For example, constructivism is currently redirected to constructive mathematics. If you’d prefer to have a separate entry for constructivism (to discuss the philosophy rather than the mathematical practice), you can simply edit constructive mathematics and remove the line (likely at the bottom of the edit box)
[[!redirects constructivism]]Now you can create constructivism as usual and any pages that had previously been redirected to constructive mathematics will now point to your new entry.
See also the official Instiki guidelines on redirects.
Since the Instiki code for hyperlinks
[link text](url)uses parenthesis, the parser apparently gets confused when the url itself contains parenthesis. To work around this one can
“escape” the parenthesis by replacing in the url
“(...)” by “%28...%29”
or
fall back to the HTML tag
<a href="url">link text</a>
or
use reference-style links
[link text][1] [1]: url
Of course, you need to replace “1” here by a distinct number (or alphanumeric string) for every distinct url on a given page (which also means that this syntax is error-prone, especially when copy-and-pasting material).
For example
[Monad (category theory)#Monads and adjunctions](http://en.wikipedia.org/wiki/Monad_%28category_theory%29#Monads_and_adjunctions)or
[Monad (category theory)#Monads and adjunctions][1]
[1]: http://en.wikipedia.org/wiki/Monad_(category_theory)#Monads_and_adjunctionsMany pages include a “floating table of contents” at the top right-hand side with links to other pages on similar topics. The lists of related pages are separate pages with names such as category theory - contents; if you want to create a new one, look at the syntax of existing ones.
To add a floating TOC to a new page, in such a way that it will be automatically collapsed until moused over, use code such as the following at the top of the source code:
+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
### Context
#### Category Theory
+-- {: .hide}
[[!include category theory - contents]]
=--
=--
=--
If you want to include multiple contents pages, you can repeat the four lines from the one starting with #### through the first =-- line.
You can also copy-and-paste a version from existing sources, such as at /nlab/source/topos, and then adjust to your needs.
You can enter basic TikZ-diagrams by (omitting the usual math delimiters such as `$$...$$' and instead)
directly opening a block of the form
\begin{tikzpicture}
…
\end{tikzpicture}
or
\begin{tikzcd}
…
\end{tikzcd}
and adding usual TikZ-code inside.
A graphical user interface for generating TikZcd code is the quiver editor at q.uiver.app. (After drawing your diagram there, click on LaTeX at the bottom to copy-and-paste the code to be inserted into the above environments.)
Beware that this functionality is a hack: The tikz-code is compiled server-side and then included as an SVG in the page’s HTML source.
In practice this means that TikZ-code does not interact with the ambient instiki-code, for instance it cannot be included inside bullet-items nor inside other math-environments. To prevent instiki‘s indentation mechanism from clashing, be sure to align the outer block of the TikZ-code to the left of the edit window.
(There used to be a claim here that
\usetikzlibrarycan be called inside thetikz-code block, but it does not seem to be the case.)
Picture:
Source:
\begin{centre}
\begin{tikzpicture}
\draw[blue, ->] (0,0) -- (1,0) -- (1,-1);
\end{tikzpicture}
\end{centre}
Single morphism:
Source:
\begin{centre}
\begin{tikzcd}
x \ar[r] & y
\end{tikzcd}
\end{centre}
Diagram of adjoint functors :
Source:
\begin{centre}
\begin{tikzcd}
\mathcal{D} \arrow[r, shift right=7pt, "R"', "\bot"] &
\mathcal{C} \arrow[l, shift right=7pt, "L"']
\end{tikzcd}
\end{centre}
As of 2019 you can format commutative diagrams in the nLab using xymatrix command, almost as you would in a LaTeX document. The only significant differences are:
Use a \begin{xymatrix} ... \end{xymatrix} block rather than a \xymatrix{...} block.
Some global parameters can be passed inside the \begin{xymatrix} tag. For example, as usual, one can use @=1.5em to increase row and column separation, replacing @ by @C (resp. @R) for column (resp. row=) separation. Thus one writes: \begin{xymatrix@=1.5em}. In addition, unlike in LaTeX, one can pass parameters in square brackets: \begin{xymatrix[font = \large, border = 2em]} or \begin{xymatrix@=1.5em[font = \large, border = 2em]}. Here the value of font controls the font size throughout the diagram, and border adds some whitespace around the figure, which is sometimes needed when using curved arrows. One can use only one of the two parameters instead of both.
Under the hood, this works by running pdflatex and then generating an SVG from the resulting pdf, which is included in the HTML source of the rendered page.
Use Tikz rather than Xymatrix if you do not have a strong preference or have not used either before. But it is fine to use Xymatrix if this is what you are used to.
Triangle:
Source:
\begin{centre}
\begin{xymatrix}
A \ar[r] \ar[dr] & B \ar[d] \\ & C
\end{xymatrix}
\end{centre}
Bent arrows:
Source:
\begin{centre}
\begin{xymatrix[border = 2pc]}
A \ar@/^2.0pc/[r] \ar@/_2.0pc/[r] & B
\end{xymatrix}
\end{centre}
Parallel arrows:
Source:
\begin{centre}
\begin{xymatrix}
A \ar@<.6ex>[r] \ar@<-.6ex>[r] & B
\end{xymatrix}
\end{centre}
2-cell:
Source:
\begin{centre}
\begin{xymatrix[font = \large]@C+2pc}
A \rtwocell^f_g{\alpha} & B
\end{xymatrix}
\end{centre}
An older workaround is to use use arrays or matrices. For example,
$$
\begin{matrix}
(f/g)& \to & A \\
\downarrow&\underset{\alpha}{\swarr}&\, \downarrow f\\
B &\underset{g}{\to} & C
\end{matrix}
$$produces
In many cases, you may wish to tweak the alignments (say, of vertical arrows), using \mathrlap{} or \mathllap{}:
is produced by
\[
\begin{matrix}
B^{\mathrlap{A}} & \longrightarrow & 1^{\mathrlap{A}} \\
\mathllap{\scriptsize{\sigma^A}}\downarrow & & \downarrow \mathrlap{\scriptsize{t^\alpha}} \\
P(B)^{\mathrlap{A}} & \underset{\chi_\sigma^A}{\longrightarrow} & P(1)^{\mathrlap{A}}
\end{matrix}
\]Matrix and array environments also accept certain options. Here is an example using a “\rowlines{solid}” option to hack a sequent derivation (much more nicely than by resorting to \frac commands):
is produced by
$$
\array{
\arrayopts{\rowlines{solid}}
X \times B \to P A\;\;\; in\; \mathbf{S} \\
X \times B \nrightarrow A\;\;\; in\; Rel(\mathbf{S}) \\
X \nrightarrow A \times B\;\;\; in\; Rel(\mathbf{S}) \\
X \to P(A \times B)\;\;\; in \; \mathbf{S}
}$$But use Tikz wherever possible.
One can upload an image to the nLab as follows.
Add [[some_picture.jpg:pic]] or [[some text that you wish to display|some_picture.jpg:pic]] to the page to which you wish to add the image. Save your edit.
Click on the ? symbol that appears after ‘some_picture.jpg’ or ‘some text that you wish to display’ on the page.
You will be sent to a page where you can upload the image.
After uploading the image, you will need to make some edit to the page to refresh it. After this, the picture should appear on the page.
The :pic functionality does not allow much configuration.Once it is uploaded, one can replace it by an imagefromfile block, such as the following.
\begin{imagefromfile}
"file_name": "FileName.xyz"
\end{imagefromfile}The contents of the block must be a valid JSON, but without curly opening and closing braces. There are several possible parameters. A common case is the following, which sets the width of the image (the height is automatically adjusted correspondingly).
\begin{imagefromfile}
"file_name": "FileName.xyz",
"width": 300
\end{imagefromfile}The default unit is pixels; to specify a different one, or to make it explicit, one uses the ‘unit’ parameter. Currently the only permitted values are “px” and “em”, which correspond to pixels and ‘em’ respectively.
\begin{imagefromfile}
"file_name": "FileName.xyz",
"width": 300,
"unit": "px"
\end{imagefromfile}Another common case is the following, which puts the image to the right of the page with the other text fitting around it, with a nice margin in between. The ‘unit’ inside the ‘margin’ block behaves in the same way as the overall width/height, in particular defaulting to pixels, but applies only to the margin.
\begin{imagefromfile}
"file_name": "FileName.xyz",
"float": "right",
"margin": {
"top": -40,
"right": 0,
"bottom": 20,
"left": 20
}
\end{imagefromfile}The full list of options is shown below. Except for “file_name”, these are all either optional or have defaults.
\begin{imagefromfile}
"file_name": "FileName.xyz",
"web": "nlab",
"width": 300,
"height": 300,
"unit": "px",
"float": "right",
"margin": {
"top": -40,
"right": 0,
"bottom": 20,
"left": 20,
"unit": "px"
},
"alt": "Some picture",
"caption": "This is some picture"
\end{imagefromfile}These should be fairly self-explanatory. The alt parameter corresponds to the <img> attribute of the same name.
Note in particular that a caption can be added. If one is floating the graphic and one uses a negative value for top in the values for margin, which is quite often a good idea, then one typically will need a positive value for bottom in order for text wrapping around the image not to obscure the caption.
Be judicious when floating graphics. It may be easier to read a page, especially on a mobile phone, if the graphic is simply placed below a paragraph rather than floating to the side of it.
Text or figures can be centred exactly as in LaTeX. For instance,
is produced by
\begin{centre}
Hello!
\end{centre}
or by the following (i.e. either UK or US spelling can be used).
\begin{center}
Hello!
\end{center}
For general information and help with Instiki, see the Instiki wiki.
Here are some useful specifics:
This is worth perusing carefully; for example, iTeX does not provide a command such as \prescript to generate left subscripts. Instead it contains the more general \multiscripts command to typeset subscripts and superscripts both to the left and right of an expression. For instance, the math mode text \multiscripts{_0^2_1}{R}{_i^j_k} produces
The Lab serves mathematical symbols as MathML. Presently the browsers with native MathML support, and hence immediate rendering of the formulas, are those based on the Gecko, Blink, and WebKit rendering engines, e.g., Firefox, Chrome/Chromium, Safari, etc.
Older unmaintained browsers like Internet Explorer, as well as a few obscure mobile and desktop browsers, fall back to rendering MathML formulas using the MathJax polyfill. This works, but is slow. On small pages it is fine, on larger pages with many formulas MathJax may take up to several minutes for rendering.
The nLab has a spam filter that checks your IP against a blacklist. The blacklists used are maintained by spamcop.net and spamhaus.org. IPs are added to these lists if they are detected doing things usually associated with computers infected with viruses. There are instructions on the webpages for finding out if your IP has been added to these lists and what to do to remove your IP from them. Three things to point out are:
Sometimes something doesn’t work quite right with the software and it bails out. If you think that you were doing something that should work, please log the error message at the nForum. The more information that you log, the easier it is for us to debug. Useful information is: your IP, the time and date, and the URL that you were trying to access.
There is actually more information contained in the HTML source of the error message (“view source”): some errors can be down to malformed input when editing a page and that can help you fix it yourself.
Most conventional search engines such as Google, Bing, Yandex, Yahoo, Baidu, DuckDuckGo, StartPage, and others allow to search the nlab by appending site:ncatlab.org to the query. If DuckDuckGo is your search engine, you can type “!nl” to search the nLab, e.g., “!nl morphism”.
The built-in search. This is via the search box at the top of every page. The distinguishing characteristics of this search are:
Instiki’s search uses regular expressions. That means you can do all sorts of fancy searches, but it also means that pages with special characters in their names are hard to search for. For instance, if you search for (n,r)-category you will come up with nothing, because Instiki interprets the parentheses as a regular expression grouping construct. To search for actual parentheses, you need to backslash them: search instead for \(n,r\)-category.
Regular expressions are a powerful way of extending search capabilities to take into account that one often wants to search for more than just a set phrase. In a regular expression, certain characters are declared to be “special” and have a particular interpretation (somewhat like TeX with its special catcodes). A special character can always be “escaped” to interpret it as an ordinary character. Thus . means “match any single character” but \. means “match a period”.
As Instiki is written in ruby, it uses the ruby version of regular expressions (each language has its own version; the differences are usually minor). The following is based on the list at ruby-doc. It has been condensed slightly to those aspects likely to be of use here:
., |, (, ), [, \, ^, {, +, $, *, and ?. To match one of these characters, precede it with a backslash. All other characters ordinarily just match themselves unless they are made somehow special by one of the special characters.\b, \Bcat matches against category and cat but cat\b only matches cat (and scat).[…]|, (, ), [, ^, $, *, ? are treated as regular characters in such a list. You can specify a range using -: thus, a-z. To include a ] or - it must come at the start of the list. A ^ at the start negates the list.\d, \s, \w\D, \S, \W. (period)(…)[…], or a (…).*ab* matches a, ab, abb, and so forth. Similarly, (cat)* matches cat, catcat, catcatcat, and so forth. This will try to match as much as possible; use *? to make it match as little as possible.+ab+ matches ab, abb, but not a. This will try to match as much as possible; use +? to make it match as little as possible.{,}{,}? to make it match as little as possible.?(Firefox - and clones - specific)
One way to do this is to install one of several firefox extensions, e.g. for Emacs or for Sublime Text, Atom, VS Code, and Vim. There are also extensions which add some basic editor features to html text areas, for instance Find & Replace for Text Editing allows you to use regular expressions and text templates.
If your favorite editor is Emacs with AucTeX, you may find the following snippet useful to put in your .emacs file:
(add-to-list 'auto-mode-alist '("/\\(www.\\)?ncatlab.org" . latex-mode))
(add-to-list 'auto-mode-alist '("/golem.ph.utexas.edu" . latex-mode))
(defun nlab-latex-fixes ()
(when (or (string-match "/\\(www.\\)?ncatlab.org" buffer-file-name)
(string-match "/golem.ph.utexas.edu" buffer-file-name))
(longlines-mode t)
(set (make-local-variable 'TeX-open-quote) "\"")
(set (make-local-variable 'TeX-close-quote) "\"")))
(add-hook 'LaTeX-mode-hook 'nlab-latex-fixes)This will tell Emacs to automatically edit nLab pages (and nCafe comments as well, for good measure) in LaTeX mode, with long lines wrapped using soft returns, and ordinary double-quotes rather than LaTeX ones.
Use the ‘Print’ link at the bottom of the page. As a shortcut in most browsers on most operating systems, hit Alt-Shift-P while the focus is in the page to go to the printable page.
(Firefox - and clones - specific)
You may wish to customize the font scheme (both for math or text) on the nLab, as well as tweak things such as the small edit box for comments. Try using the Stylish add-on if you are using Firefox; Stylish is a plug-in for firefox enabling you to customize websites; it is available here.
Currently, the following stylish themes are available:
A current git repository of the source code for nLab pages is available at https://github.com/ncatlab/nlab-content and a current git repository of the compiled HTML code for nLab pages is available at https://github.com/ncatlab/nlab-content-html.
Last revised on April 18, 2025 at 22:15:52. See the history of this page for a list of all contributions to it.