4
votes
1answer
427 views

Which E_∞-spaces are homotopy colimits of k-truncated E_∞-spaces?

This question is closely related to my previous question about modules over truncated sphere spectra, in particular, it has the same motivation. Recall that every space (or ∞-groupoid) can be ...
1
vote
2answers
288 views

Cech cohomology as a colimit over maps to a CW complex

Given a topological space $X$, we consider the following category $\mathsf{CW}_{X\to}$. The objects are finite CW complexes $Y$ equipped with a continuous map $X\to Y$. The morphisms are continuous ...
9
votes
2answers
413 views

Fubini theorem for hocolim.

I wanted to ask the following question, Suppose $\mathbf{M}$ a cof generated model category and $I,~J$ two small categories. Suppose that $F:J\rightarrow \mathbf{M}^{\mathrm{I}}$ is a functor. Is it ...
2
votes
2answers
789 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 ...
13
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 ...