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Nov 2, 2018 at 2:45 history edited John Berman CC BY-SA 4.0
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Oct 31, 2018 at 1:15 comment added K.J. Moi If you take $I$ to be the standard simplicial circle then I think the functor category has infinitely many isomorphism classes. However the indexing simplicial set is not a quasi-category, so this is maybe not what you want.
Oct 30, 2018 at 17:48 answer added Phil Tosteson timeline score: 2
Oct 30, 2018 at 16:38 history edited John Berman CC BY-SA 4.0
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Oct 30, 2018 at 16:31 history edited John Berman CC BY-SA 4.0
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Oct 30, 2018 at 16:29 comment added John Berman You're right! I meant to sum over each equivalence class of $X\in I$. I will correct that.
Oct 30, 2018 at 16:08 comment added Tom Goodwillie I'm not sure I understand your definitions, but it seems that if $I$ is an ordinary category then the left hand side is invariant under equivalence of categories while the right hand side depends on the object set.
Oct 30, 2018 at 15:36 history asked John Berman CC BY-SA 4.0