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2
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0answers
229 views

Colimit of an etale diagram of schemes

It is known that the category of schemes is not cocomplete (e.g. see this question: Colimits of schemes). However, do diagrams of schemes for which every morphism is etale have colimits? More ...
4
votes
1answer
481 views

colimits of spectral sequences

I'm looking for some references about colimits of spectral sequences. More precisely: let $X : I \longrightarrow \cal{C}$ be a functor from a filtered category $I$ to the category of double cochain ...
1
vote
2answers
406 views

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 ...
3
votes
2answers
1k 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
520 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 ...
12
votes
1answer
1k 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
707 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 ...
9
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
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9answers
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 ...