# Tagged Questions

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### Is there a tricategory of bicategories and biprofunctors?

Background There is a bicategory where the objects are categories, the 1-morphisms are profunctors, and the 2-morphisms are morphisms of profunctors. The non-obvious part of this assertion is that ...
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### Decomposing a large colimit as a pushout of smaller colimits

I would like to find a reference in the literature for the following result. I have it on high authority that it isn't in 'Categories for the Working Mathematician' and I can't find it in Borceux's ...
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### 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 ...
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### 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 ...
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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 ...