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11h
accepted Are PL-homeomorphic manifolds diffeomorphic?
2d
awarded  Yearling
Apr
14
asked Are PL-homeomorphic manifolds diffeomorphic?
Apr
1
accepted When is an object in a linear or abelian category simple? Or: How should I define fusion categories?
Mar
25
comment When is an object in a linear or abelian category simple? Or: How should I define fusion categories?
But you agree that "strongly simple" implies simple?
Mar
24
asked When is an object in a linear or abelian category simple? Or: How should I define fusion categories?
Mar
17
comment Can two smooth categories be equivalent if their object manifolds aren't diffeomorphic or homotopy equivalent?
@Qiaochu, $G//H \simeq H$ as plain categories, but I was hoping that might not be true as smooth categories because their object spaces are different.
Mar
16
comment Can two smooth categories be equivalent if their object manifolds aren't diffeomorphic or homotopy equivalent?
@QiaochuYuan, my motivation is to understand whether smooth action groupoids are actually equivalent to their stabiliser Lie groups (viewed as a smooth category). I was hoping that the correct notion of equivalence forbids e.g. your example, so that what you say would hopefully not be a smooth equivalence.
Mar
16
comment Can two smooth categories be equivalent if their object manifolds aren't diffeomorphic or homotopy equivalent?
@ZhenLin, what possible definitions are there, then?
Mar
16
asked Can two smooth categories be equivalent if their object manifolds aren't diffeomorphic or homotopy equivalent?
Mar
12
comment Can I recover a group by its homomorphisms?
@Qiaochu, where can I learn more about whether fundamental groups of closed 4-manifolds are residually finite?
Mar
12
comment Can I recover a group by its homomorphisms?
Ok, memory comes back. This does seem to be the interesting case. Still, I think you should ask that question.
Mar
12
comment Can I recover a group by its homomorphisms?
Thanks, but I don't even know what "residually finite" is, so if you want a separate question on that matter, go ahead. Edit: I see, that's the thing Qiaochu talked about in the first comment to the question.
Mar
12
comment Can I recover a group by its homomorphisms?
Or you could post it ;)
Mar
11
comment Can I recover a group by its homomorphisms?
Given that your proof feels a bit like magic, no I don't :I
Mar
11
comment Can I recover a group by its homomorphisms?
Shouldn't it be $n_H$?
Mar
6
accepted Does “modular category” make sense without saying “abelian” or “linear”?
Mar
6
asked Does “modular category” make sense without saying “abelian” or “linear”?
Mar
6
revised Why isn't the use category theory for graph transformation more prominent?
added 7 characters in body
Mar
2
awarded  Popular Question