# nLab 2008 changes

### Archive

Archive of changes made during 2008. The substantive content of this page should not be altered. For past versions of this page beyond its own history, start here and work backwards.

• Toby (2008-12-31): I have a precise definition of evil, so I put that in.

• Urs (Dec 31): started FQFT, currently just a commented list of literature trying to give an impression of the idea. Also adjusted quantum field theory and created vertex operator algebra.

• Urs (Dec 30): started entries on groupoidification and quantum field theory.

• John (Dec 29): I’m going to make a little entry about the term evil.

• Toby (Dec 28): I added a bunch of stuff about apartness relations. (Most of it is probably even correct.) I tried to say as much as I could in terms of enriched category theory, but the topic is really analysis.

• John (Dec 23): I expanded the entry on action groupoid and started one for action and automorphism. In the process I noted that Urs seems to be using $Sets$ for the category of sets, while most mathematicians use Set. We should settle (pardon the pun) this issue. I hope that someday there will be lots of entries on specific important categories, listing some of the special features of these categories.

• Urs (Dec 23): continued completing “lits of related entries” in the main entries linked to from the HomePage: did Lie theory and differential geometry

• Urs (Dec 23): started creating nonabelian algebraic topology and crossed complex and expanded a bit related entries linked to from there. Am hoping we can eventually present more details here.

• Urs (Dec 22): started replying to a question Eric raised at General Discussion about the shape of cells used in higher categories. Created geometric shapes for higher structures with a discussion of the general idea and linked to globular set, simplicial set and cubical set from there. Still plenty of room to add details. Am planning to give details on the monoidal structure on cubical sets and the induced Crans-Gray tensor product on $\omega$-categories.

• Urs (Dec 20): I started to add alphabetical lists of all related entries to the big headline entries that are linked to from the sidebar of the HomePage. So far I did this in category theory, sheaf and topos theory, foundations and higher category theory. It might be good if each time we create a new entry we think about adding the correspondin link to one of these general lists.

• Urs (Dec 20): I replied to the discussion at monoidal category on “Where does all this structure and coherence come from?” by adding a subsection on how all this comes from the general concept of $\infty$-lax functor for which one formalization can be given in terms of orientals and Street’s descent. The pentagon identity is precisely the fourth oriental!

• Toby (Dec 20–23): I won't do anything, since I'll be travelling. (Just in case you wonder where I am.)

• Urs: Thanks for the info, Toby. Myself, I will probably be online sporadically over the holidays.
• John (Dec 20): I sketched the definitions of monoidal category, braided monoidal category, and symmetric monoidal category and gave links to full definitions and explanations. Is someone good enough at drawing diagrams in this environment to draw the necessary diagrams — e.g. pentagon and hexagon identity?

• Toby (Dec 20): More on Grothendieck topos and well-pointed topos, including definitions that are correct in constructive mathematics.

• Urs: recently, after Eric had requested an “arrow-theoretic” description of category algebra and of graded vector spaces, I had provided a description in terms of bi-branes and remarked that this is part of a bigger picture. That bigger picture, together with these examples, is now described over in my private area at Nonabelian cocycles and their quantum symmetries. For completeness I have added links to that to category algebra and graded vector space. Instead of giving the impression of forcing this relation to my work upon these entries, I would like you to understand this as an invitation to check and, if necessary, criticize.

• Urs: I tried to flesh out tensor product and module a bit further, providing more details and attempting to bring the different points of view together. Check.

• Toby Bartels: I just expanded tensor product, enough to include the example that links to it (without circularity).

• Urs: I expanded on the entry action groupoid that Eric started.

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Last revised on August 23, 2015 at 22:29:32. See the history of this page for a list of all contributions to it.