The colimits tag has no usage guidance.

**2**

votes

**0**answers

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

**1**answer

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

**2**answers

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

**2**answers

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

**2**answers

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

**1**answer

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

**2**answers

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

**2**answers

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

**9**answers

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 ...