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Results tagged with simplicial-stuff
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user 10605
For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
10
votes
An abstract nonsense proof of the Hurewicz theorem
Here is a sketch of the proof, some details filled below. All categories
are $(\infty,1)$-categories and all functors are $(\infty,1)$-functors
unless specified otherwise. The notion of a topological …
- 4,780
9
votes
1
answer
744
views
Equivariant homotopy, simplicially
It is a classic result of Kan that the homotopy categories (with appropriate model structures) of simplicial sets and of topological spaces (in fact, one could only care about CW-complexes) are equiva …
- 4,780
4
votes
Accepted
A groupoid which is homotopy equivalent to $BG$
Let $X = BG \times [0; 1]$, then $\ast_a = (\ast; 0)$, $\ast_b = (\ast; 1)$, $\gamma$ is the image of $[0;1]$, $f_a$ is any choice of path in the class of $a$ and $f_b$ is any choice of path in class …
- 4,780