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Results tagged with higher-category-theory
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user 2181
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
8
votes
Joins of simplicial sets
It might be helpful to work through some simple examples. You probably know that Δn ★ Δk = Δn+k+1. This has to do with the ordinal sum: one way of defining joins is as a restriction of the monoidal st …
- 1,569
9
votes
Accepted
Follow up: Is continuity preserved when taking comma object?
Our paper specializes to the case of 1-categories with (co)limits and (co)limit-preserving functors, not to 2-categories.
But surely this is true. I'm defining the comma object in the 2-category of …
- 1,569
18
votes
Model independent proof of colimit formula for left Kan extensions
Dominic Verity and I have been working to develop model independent foundations of $(\infty,1)$-category theory. Our aim at present isn't to cover all models of $(\infty,1)$-categories but only the "b …
- 1,569
6
votes
Accepted
Proof that a quasicategory is equivalent to the homotopy coherent nerve of a simplicial cate...
Sorry, we should have made this more clear. One proof appears as Theorem 7.2.2 in our previous paper in this series, The comprehension construction. As suggested by others, it follows from a suitably …
- 1,569