The colimits tag has no wiki summary.

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### Tot and colimits

This must be a well-known exercise with spectral sequences, but I don't know a reference for it. I'm trying to figure out when does $Tot$ commute with colimits.
More precisely, let $X$ be a double ...

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### 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
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### 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 ...

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### 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 $G_a$,
$\int^AG_a$,
...

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### 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
...

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### 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 ...

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### 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 ...