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I worked on brushing up (infinity,1)-category a little
mostly I added in a section on homotopical categories, using some paragraphs from Andre Joyal's message to the CatTheory mailing list.
in this context I also rearranged the order of the subsections
I removed in the introduction the link to the page "Why (oo,1)-categories" and instead expanded the Idea section a bit.
added a paragraph to the beginning of the subsection on model categories
added the new Dugger/Spivak references on the relation between quasi-cats and SSet-cats (added that also to quasi-category and to relation between quasi-categories and simplicial categories)
brief category:people-entry for hyperlinking references at Deligne-Mumford stack and orbifold
added this pointer:
Was looking for references to point readers to for background on the idea that DM-stacks and orbidfolds are essentially the same thing, realized in two different geometric categories (up to a list of inessential technical conditions). This is the best I have found so far. If anyone knows further references along these lines, please drop a note.
stub, just for completeness of the Happy Family
started universal exceptionalism
related discussion is taking place on g+ here
For completeness, so that we now have this list:
I am slowly creating a bunch of entries on basic concepts of equivariant stable homotopy theory, such as
At the moment I am mostly just indexing Stefan Schwede’s
I have added pdf-links to the reference
and promoted this to the top of the list, since I suppose this is the most comprehensive account that a reader might want to go to first. Will also edit accordingly at topological stack
brief category:people-entry for hyperlinking references at orbifold and hyperbolic manifold, in particular to this excellent book:
I kept being annoyed about the nature of discussion of the “multiverse” (the one in cosmology, not the one in set theory). Now I thought instead of steadily being annoyed, I should start an Lab entry that does it better. So I did now (or tried to), at multiverse.
Todd,
you added to Yoneda lemma the sentence
In brief, the principle is that the identity morphism is the universal generalized element of . This simple principle is surprisingly pervasive throughout category theory.
Maybe it would be good to expand on that. One might think that the universal property of a genralized element is that every other one factors through it uniquely. That this is true for the generalized element is a tautological statement that does not need or imply the Yoneda lemma, it seems.
brief category:people-entry for hyperlinking references at moonshine, duality between heterotic and type II string theory, Riemannian orbifold and maybe elsewhere
Added some examples to allegory, including that of modular lattice as one-object allegory.
added more references to 2-spectral triple (as far as I can see Jürg Fröhlich with his students was the first to try to formalize this to some extent)
felt like archiving a quote by Paul Taylor somewhere, it is now at folklore.
Besides being funny, it is actually a useful comment for the newbie, and so I linked to it from category theory.
I am beginning to give the entry FQFT a comprehensive Exposition and Introduction section.
So far I have filled some genuine content into the first subsection Quantum mechanics in Schrödinger picture.
But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.
I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.