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\section*{2009 February changes}

\hypertarget{archive}{}\subsubsection*{{Archive}}\label{archive}

[[!include all changes]]

Archive of changes made during February 2009. The substantive content of this page should \textbf{not} be altered. For past versions of this page beyond its own history, start \href{http://ncatlab.org/nlab/revision/2009+June+changes/314}{here} and work backwards.


\vspace{.5em} \hrule \vspace{.5em}
\hypertarget{20090228}{}\section*{{2009-02-28}}\label{20090228}

\begin{itemize}%
\item [[Tim Porter|Tim]] Added new material to [[crossed square]].

\end{itemize}
\hypertarget{20090227}{}\section*{{2009-02-27}}\label{20090227}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item edited [[action]] a bit more -- but that entry is still not nice


\item extended [[geometric function theory]]


\item continued replying to [[Mike Shulman|Mike]] at [[hyperstructure]]



\end{itemize}


\end{itemize}
\hypertarget{20090226}{}\section*{{2009-02-26}}\label{20090226}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item created [[action of a category on a set]] in reply to a question raised over at \emph{Secret Blogging Seminar} \href{http://sbseminar.wordpress.com/2009/02/25/delignes-%e2%80%9cla-categorie-des-representations-du-groupe-symetrique-s_t-lorsque-t-n%e2%80%99est-pas-un-entier-naturel%e2%80%9d/#more-1487}{here}

\end{itemize}

\item [[Andrew Stacey|Andrew]]

\begin{itemize}%
\item Created a [[request for help]] page. There are query boxes scattered all over the lab and I think that it ought to be a priority to answer these. A query on a page might be answerable by someone not an expert in what's on that page (or even not interested in what's on that page) - in fact, that's highly likely. Flagging questions on this page (i.e., Latest Changes) is also less than optimal as it's not clear who might be able to answer them (and probably not everyone checks this page). I freely admit that I'm doing this because no-one seems bothered in my questions on [[Froelicher space]]s which are, in fact, more general category theory than specifics to Fr\"o{}licher spaces.

I've added it to the sidebar (and taken off [[General Discussion]]).



\end{itemize}


\end{itemize}
\hypertarget{20090225}{}\section*{{2009-02-25}}\label{20090225}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item created [[enriched functor category]] for completeness


\item added a bit more details and references concerning the SSet homotopy limit at [[weighted limit]]


\item after checking with [[Mike Shulman|Mike]] added details of the definition of homotopy limits in terms of weighted limits in the [[SSet]]-enriched context to [[weighted limit]]; also edited accordingly the section \emph{local definition} at [[homotopy limit]] and created a section on weighted limits at [[representable functor]]



\end{itemize}


\end{itemize}
\hypertarget{20090224}{}\section*{{2009-02-24}}\label{20090224}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item have a question at the end of [[weighted limit]] for the homotopy coherency experts


\item created [[weighted limit]]


\item added references to [[sheaf]] and [[simplicial set]]



\end{itemize}


\end{itemize}
\hypertarget{20090223}{}\section*{{2009-02-23}}\label{20090223}

\begin{itemize}%
\item [[Tim Porter|Tim]]:

\begin{itemize}%
\item Created an entry on the Conduch\'e{} decomposition of the group of $n$-simplices of a simplicial group: [[decomposition theorem for simplicial groups]]. (An idea for renaming this entry would be welcome!)
\item Edited [[group T-complex]].

\end{itemize}


\end{itemize}
\hypertarget{20090219}{}\section*{{2009-02-19}}\label{20090219}

\begin{itemize}%
\item [[Mike Shulman|Mike]]: created [[n-fibration]].

Why do I think of the Beach Boys every time I read the word $n$-fibrations? - Eric


\item [[Ronnie Brown|Ronnie]]: over the last two days, created [[compositions in cubical sets]] which gives the basic definitions and axioms for cubical sets with compositions and connections, (and inverses), with the example of the cubical singular complex in mind.



\end{itemize}
\hypertarget{20090218}{}\section*{{2009-02-18}}\label{20090218}

\begin{itemize}%
\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Created [[Euler characteristic]] in order to ask a question there.

\end{itemize}


\end{itemize}
\hypertarget{20090217}{}\section*{{2009-02-17}}\label{20090217}

\begin{itemize}%
\item [[Toby Bartels]]:

\begin{itemize}%
\item Separated [[equivalence of categories]] from [[equivalence]].
\item Basically copied [[2-category]] to [[3-category]], then added a bit to the end of each to make the difference nontrivial. Also created [[strict 3-category]] along similar lines, although it's still rather short.

\end{itemize}

\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Introduced the terminology \emph{strict [[homotopy limit]]} by analogy with [[strict 2-limit]].


\item Rearranged [[homotopy pullback]] to make it fit better with [[homotopy limit]].



\end{itemize}


\end{itemize}
\hypertarget{20090216}{}\section*{{2009-02-16}}\label{20090216}

\begin{itemize}%
\item [[Toby Bartels]]:

\begin{itemize}%
\item Fixed links to [[equivalence]] that should really be to [[weak equivalence]].
\item Separated [[Segal space]] from [[complete Segal space]].

\end{itemize}

\item [[Mike Shulman|Mike]]: asked a question about [[horizontal categorification]].



\end{itemize}
\hypertarget{20090215}{}\section*{{2009-02-15}}\label{20090215}

\begin{itemize}%
\item [[Tim Porter|Tim]]: Added the construction of $\overline{W}$, the classifying space construction for simplicial groups to the entry for [[simplicial group]].


\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item created [[topological T-duality]]


\item created [[homotopy pullback]]


\item created [[weak equivalence]]


\item replied at [[dg-category]]



\end{itemize}


\end{itemize}
\hypertarget{20090214}{}\section*{{2009-02-14}}\label{20090214}

\begin{itemize}%
\item [[Ronnie Brown|Ronnie]] Added entries on C. [[Ehresmann]] and on [[Grothendieck]]. The second probably should be expanded, but it has a link to a good account.


\item [[Tim Porter|Tim]]: Asked a question in [[dg-category]] as to the degree of the differentials. We may need a convention on this.


\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item added To\"e{}n-Vezzosi proposal $2Vect := Ch(Vect)-Mod$ to [[2-vector space]] and created [[dg-category]] accompanying this

\end{itemize}


\end{itemize}
\hypertarget{20090213}{}\section*{{2009-02-13}}\label{20090213}

\begin{itemize}%
\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Incorporated the reference Tim suggested at [[homotopy limit]].


\item Replied at [[strict 2-limit]] and [[comma category]].



\end{itemize}

\item [[Tim Porter|Tim]]:

\begin{itemize}%
\item Added something to [[homotopy limit]] in part to provide a possible `old' reference in reply to Urs and Mike below.
\item Started adding some summaries of results to [[group T-complex]].

\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item Imposed the convention for a group $G$, that $\mathcal{B}G$ is a space while $\mathbf{B}G$ is a groupoid, on [[classifying space]] and [[homotopy 1-type]] (although the groupoid has disappeared from that one), to hopefully reduce confusion.
\item Linked [[FAQ]] and [[HowTo]] from one another.
\item Terminological notes at [[strict 2-limit]] and [[comma category]].

\end{itemize}

\item [[Mike Shulman|Mike]]: Urs, in my biased opinion, the reference for the [[homotopy limit]] comparison that I find easiest to understand is my own paper (reference added). Of course the fact has been known for a long time; I don't even know whether there's any ``original'' source one could cite.



\end{itemize}
\hypertarget{20090212}{}\section*{{2009-02-12}}\label{20090212}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]: at [[homotopy limit]] I am asking for further details and/or literature on the ``central theorem'' which identified local and global definition


\item [[Mike Shulman]]:

\begin{itemize}%
\item Added what I think is a more standard viewpoint to [[classifying space]], although there are so many different meanings of that term.


\item Created [[comma object]] and started messing around with using SVG for diagrams instead of {\colorbox[rgb]{1.00,0.93,1.00}{\tt ~array}}. It's more work but it sure does look nicer (in the output, anyway).

[[Urs Schreiber|Urs]]: looks good! We should have at [[FAQ]] a brief instruction for how to proceed to produce such diagrams (which software to download, how to get nicely typeset labels, etc.)

Mike: I gave it a [[FAQ|try]], but I don't have any great wisdom to impart; I just played around with the XML until it worked. If there is software that can do this for us that would be great (until someone manages to write an xypic-to-svg converter).



\end{itemize}


\end{itemize}
\hypertarget{20090211}{}\section*{{2009-02-11}}\label{20090211}

\begin{itemize}%
\item [[Toby Bartels]]:

\begin{itemize}%
\item Agreed with Mike at [[large site]].
\item Replied to Andrew at [[Toby Bartels]].

\end{itemize}

\item [[Mike Shulman|Mike]]

\begin{itemize}%
\item I like the edits at [[2-limit]] and [[strict 2-limit]], so I removed the comments (but anyone else with opinions, feel free to restart the discussion).


\item Naming question for [[large sheaf]].


\item Answered at [[model structure on simplicial presheaves]]



\end{itemize}

\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item have a question for [[Mike Shulman|Mike]] at [[model structure on simplicial presheaves]]


\item created [[Bousfield localization]]



\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item Comments (with related edits) at [[2-limit]] and [[strict 2-limit]].
\item Expanded [[section]] and wrote [[retraction]] following it; similarly wrote [[split monomorphism]] following [[split epimorphism]].
\item Separated [[k-tuply monoidal (n,r)-category]] from [[periodic table]].
\item Linked to [[Pursuing Stacks]] from [[infinity-stack]] so it won't be an orphan. People more familiar with \emph{Pursuing Stacks} than I am may want to link to it in other ways.

\end{itemize}


\end{itemize}
\hypertarget{20090210}{}\section*{{2009-02-10}}\label{20090210}

\begin{itemize}%
\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item created [[sheaves on large sites]] mainly to ask the question which I ask there


\item created [[model structure on simplicial presheaves]], [[model structure on simplicial sheaves]]



\end{itemize}

\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Wrote about effective-epimorphic sieves at [[subcanonical coverage]], by way of answering questions about [[anafunctor]]s.
\item Wrote [[comma category]]. We should probably be consistent between [[under category]]/[[coslice category]] and [[slice category]]/[[over category]] about which is the page and which is the redirect. I'm pulling for slice and coslice myself.

\end{itemize}

\item [[Andrew Stacey|Andrew]]

\begin{itemize}%
\item Started the [[FAQ]]. (The link on [[HomePage]] could possibly be removed - I put it there to start the [[FAQ]] but then also put a link in the sidebar.)
\item Okay, only a minor point: I corrected the syntax of the query block on the [[HowTo]] page. The syntax that was there works, but is not the ``standard'' syntax as defined by the \href{http://maruku.rubyforge.org/proposal.html}{maruku filter}.

\end{itemize}

\item [[Toby Bartels]]

\begin{itemize}%
\item Finally contributed to the discussion at [[anafunctor]].
\item Asked a question at [[subcanonical coverage]].
\item Wrote [[finite group]], since they're mentioned on [[profinite group]].
\item Clarified [[essentially algebraic theory]] a bit.

\end{itemize}

\item [[David Roberts]]

\begin{itemize}%
\item Continued discussion with Mike at [[anafunctor]], and moved the discussion to its own section. I disagreed about the use of `'regular epimorphism'` for covers in categories without all pullbacks.
\item Discussion at [[generalized smooth space]], and created (a very sketchy!) page [[profinite group]].

\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item Fixed the theorem environments at [[cat-1-group]] (you need six hash marks).
\item Defined $(n,r)$-fold categories at [[n-fold category]], just because I could.

\end{itemize}

\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item created [[Courant Lie algebroid]]


\item reacted to [[Toby Bartels|Toby]]`s remark at [[n-fold category]] by incorporating it and removing the query box



\end{itemize}


\end{itemize}
\hypertarget{20090209}{}\section*{{2009-02-09}}\label{20090209}

\begin{itemize}%
\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Replied at [[internal logic]].
\item Merged the discussion at [[directed set]] into the entry and removed the discussion. Writing [[locally presentable category]] and [[accessible category]] is on my to-do list, if no one beats me to it.
\item Raised an objection at [[entire relation]].

\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item Removed the discussion at [[internal logic]] and [[entire relation]] (which I thought I'd already corrected!), since Mike is right and I'm satisfied.
\item Wrote [[entire relation]] and [[functional relation]] (but not yet [[relation]]!).
\item Asked a question about $n$-fold groupoids at [[n-fold category]].

\end{itemize}

\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item fixed the mistake at [[interval object]] that [[Toby Bartels|Toby]] spotted and added a little bit of dicussion


\item added Berger-Moerdijk's definition to [[interval object]]



\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item Made an objection at [[interval object]].
\item Talked to Mike at [[directed set]], [[weak limit]], and [[internal logic]].

\end{itemize}

\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Replied to Toby at [[directed set]], [[internal logic]], and [[familial regularity and exactness]].


\item Created [[weak limit]].



\end{itemize}


\end{itemize}
\hypertarget{20090208}{}\section*{{2009-02-08}}\label{20090208}

\begin{itemize}%
\item [[Toby Bartels]]: Did some work on [[directed object]], which I think should have half spun off to [[undirected object]].


\item [[Tim Porter|Tim]]:

\begin{itemize}%
\item Created an entry on [[Dwyer-Kan loop groupoid]].

\end{itemize}

\item [[Toby Bartels]]:

\begin{itemize}%
\item A comment at [[directed space]], which led me to write [[directed set]] just to clarify terminology.
\item Somewhat incorporated [[Ronnie Brown]]'s remark on [[geometric shapes for higher structures]].
\item Comments on [[pospace]] and [[cartesian monad]].
\item Standardized the notation as $\Simp{C}$ for the category of [[simplicial object]]s in $C$, as on [[SimpSet]], [[simplicial set]] (where I dropped an unrelated note to Tim), [[simplicial group]], etc.
\item Explained where the name of [[Galois connection]] comes from.
\item Added some details to [[cobordism]].
\item Wrote [[Practical Foundations]] about Paul Taylor's book and linked it from [[internal logic]] (where I also conversed with Mike).
\item I really like [[familial regularity and exactness]], which confirms all my prejudices about regularity and exactness; I have a small, largely irrelevant, question.
\item I separated [[join]] and [[meet]] from [[union]] and [[intersection]] (which are terms that I'd use only for subobjects).

\end{itemize}


\end{itemize}
\hypertarget{20090207}{}\section*{{2009-02-07}}\label{20090207}

\begin{itemize}%
\item [[Ronnie Brown]]: \emph{I edited the discussion in [[fibration]] to give a reference to work of P.R. Heath on operations of the paths on the base on the fibres, a groupoid operation up to homotopy.}


\item [[Toby Bartels]]: I'm back! I'll be slowly catching up. So far, I've simply read \textbf{latest changes} and extended Andrew's navigation links for the archive. (So it looks like the sort of thing that daily updated websites create automatically using PHP, except that I did it all laboriously by hand!)



\end{itemize}
\hypertarget{20090206}{}\section*{{2009-02-06}}\label{20090206}

\begin{itemize}%
\item [[Jocelyn Paine|Jocelyn]]: edited the [[product]] page to link to an interactive demonstration written to use the same notation as in [[product]].


\item [[Mike Shulman|Mike]]: responded to all of David's edits.


\item [[David Roberts]]:

\begin{itemize}%
\item Edited [[anafunctor]] to clean up conditions on covers, and some explanations of what each one is for.


\item Created the page [[Grothendieck pretopology]]


\item Added mention of Dold fibration on the page [[fibration]].



\end{itemize}


\end{itemize}
\hypertarget{20090205}{}\section*{{2009-02-05}}\label{20090205}

\begin{itemize}%
\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Continued discussion with Urs at [[hyperstructure]].


\item Moved [[thin]] to [[thin element]] in line with the [[HowTo|naming convention]] that page names be singular nouns. Also added some other contexts in which ``thinness'' appears.



\end{itemize}

\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item replied to [[Mike Shulman|Mike]] at [[hyperstructure]]

\end{itemize}


\end{itemize}
\hypertarget{20090204}{}\section*{{2009-02-04}}\label{20090204}

\begin{itemize}%
\item [[Ronnie Brown]]

\begin{itemize}%
\item added discussion of \emph{strict versions of higher homotopy groupoids} to [[fundamental infinity-groupoid]]

\end{itemize}

\item [[Urs Schreiber|Urs]]:

\begin{itemize}%
\item added a ``laboratory section'' to [[hyperstructure]] in which I am proposing a formalization of the concept


\item created [[dagger category]]; started filling [[dagger compact category]] with content



\end{itemize}


\end{itemize}
\hypertarget{20090203}{}\section*{{2009-02-03}}\label{20090203}

\begin{itemize}%
\item [[Andrew Stacey|Andrew]]

\begin{itemize}%
\item Implemented the archive of latest changes (scroll down to the bottom of this page to get the link)
\item Added a fair bit more on Isbell Duality in [[Froelicher space]]s. A few more general queries for those a little more versed in the lore of categories than me.

\end{itemize}


\end{itemize}
\hypertarget{20090202}{}\section*{{2009-02-02}}\label{20090202}

\begin{itemize}%
\item [[Eric Forgy|Eric]]

\begin{itemize}%
\item created [[Position, Velocity, and Acceleration]] to help augment the discussion going on at the \href{http://golem.ph.utexas.edu/category/2009/01/the_third_time_is_the_charm.html#c021749}{n-Cafe}

\end{itemize}

\item [[Andrew Stacey|Andrew]]: continued with [[Froelicher space]]s. In particular, laid out some of the details of the Isbell duality proof.


\item [[Urs Schreiber|Urs]]

\begin{itemize}%
\item added as a further example the computation of $holim(\mathbf{B}H \to \mathbf{B}G \leftarrow \mathbf{B}H) \simeq H \backslash\backslash G // H$ to [[homotopy limit]]


\item many thanks to [[Mike Shulman|Mike]] and [[Timothy Porter|Tim]] for all the further details at [[homotopy limit]]!


\item re [[Mike Shulman|Mike]]`s suggestion: yes, I'd be in favor of archiving the latest changes list here more frequently



\end{itemize}

\item [[Mike Shulman|Mike]]:

\begin{itemize}%
\item Answered Urs's question in a very long-winded way by adding lots of stuff to [[homotopy limit]].
\item What would people think about rotating (i.e. archiving) the [[latest changes]] every month, rather than every year? It's pretty big right now and it will probably be immense by next December.

\end{itemize}


\end{itemize}
\hypertarget{20090201}{}\section*{{2009-02-01}}\label{20090201}

\begin{itemize}%
\item [[Andrew Stacey|Andrew]]: After crashing the [[HomePage|nLab]] 3 times I've finally managed to upload something on [[Froelicher space|Frolicher spaces]]. Something is seriously wrong with my syntax - if no one's taken pity on me and cleaned it up I'll do so myself tomorrow. More importantly, I have a few queries for the more experienced categorists so I'd appreciate someone taking a look at those for me.


\item [[Urs Schreiber|Urs]]: thanks, [[Mike Shulman|Mike]], very useful. Is anything similar known for 3-categories?



\end{itemize}

\vspace{.5em} \hrule \vspace{.5em}
[[2008 changes|First list]] --- [[2009 January changes|Previous list]] --- [[2009 March changes|Next list]] --- \href{http://www.math.ntnu.no/~stacey/Mathforge/nForum/?CategoryID=5}{Current list}


\vspace{.5em} \hrule \vspace{.5em}
category: meta



\end{document}