The tag has no wiki summary.

learn more… | top users | synonyms

3
votes
2answers
895 views

Simple examples of homotopy colimits

I am following the explicit construction of homotopy colimits as described by Dugger in the paper: "Primer on homotopy colimits", which can be found here: http://www.uoregon.edu/~ddugger/hocolim.pdf ...
7
votes
2answers
491 views

Coend computation continued

This is a follow-up question to this coend computation. Here's an attempt at a slightly simpler computation: $\int^{a \in A} \mbox{hom_A(a,a)}$ This should be similar to the trace operator. In ...
10
votes
1answer
945 views

Coend computation

Let $F:A^{\mbox{op}} \to \mbox{Set}$ and define $G_a:A\times A^{\mbox{op}} \to \mbox{Set}$ $G_a(b,c) = \mbox{hom}(a,b) \times F(c)$. I think the coend of $G_a$, $\int^AG_a$, ...
1
vote
2answers
669 views

On limits and Colimits

I want to ask a stupid question. I wonder whether following morphism exists in general Let I be an infinite set. i belongs to I Hom(A,colimBi)--->limHom(A,Bi) and ...
8
votes
2answers
1k views

Exactness of filtered colimits

Are filtered colimits exact in all abelian categories? In Set, filtered colimits commute with finite limits. The proof carries over to categories sufficiently like Set (i.e. where you can chase ...
14
votes
8answers
2k views

References for homotopy colimit

(1) What are some good references for homotopy colimits? (2) Where can I find a reference for the following concrete construction of a homotopy colimit? Start with a partial ordering, which I will ...