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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

4 votes
Accepted

Is it reasonable to define `poset homotopy' as a `natural transformation of posets'?

This is an interesting line of questions, but I think it doesn't quite work as stated. First off, your notion of "homotopy" is not an equivalence relation (as far as I understand it), so it won't agr …
Dylan Thurston's user avatar
16 votes

Why is a 2d TQFT formulated as a functor?

There are interesting examples where the duality you're trying to bake in does not hold. In particular, the 3+1 dimensional (pseudo-)TQFTs coming from Seiberg-Witten theory in 4 dimensions do not hav …
Dylan Thurston's user avatar