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

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Realization of a bisimplicial set

I think the easiest way to see it is that : $|X|_k=\cup_n (X_{n,k} \times \Delta[n]_k)/\sim$ subject to the following equivalence relation $(d_ix,p) \sim (x,d_ip), (x,p) \in X_{n,k} \times \Delta[n-1 …
Ali Abdallah's user avatar
0 votes
4 answers
2k views

Realization of a bisimplicial set

Hello, I just need some clarification (or a good reference) for the definition of the realization of a bisimplicial set, this is what i have when $X$ is a bisimplicial set its realization is $\cup_n …
Ali Abdallah's user avatar
1 vote
0 answers
153 views

Pushout of the skeleton of homotopy colimit of diagrams

First of all let me define what homotopy colimit i'm talking about. Let F be a functor from a small category to the category of simplicial set, the homotopy colimit is the simplicial realization of th …
Ali Abdallah's user avatar