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Results tagged with simplicial-stuff
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user 8032
For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
2
votes
Accepted
Relating two notions of geometric realization
Regarding
What is the relation between $|K|$ and $X$, more specifically between $|\sigma|$ and $X_\sigma$ for each simplex $\sigma \in K$?
It seems to me that one can build an intermediate space …
- 18.5k
4
votes
Accepted
realization of maps between classifying spaces of categories
Here's a counterexample. Let $M$ be a discrete monoid which is not a group. Consider the
map
$$
M = \hom (\Bbb N, M) \to \text{maps}_{*}(B\Bbb N , BM) = \Omega BM
$$
($\Omega BM =$ the based loops of …
- 18.5k
8
votes
Accepted
Degeneracies for semi-simplicial Kan complexes
The answer to (1) is to be found in
Rourke, C. P.; Sanderson, B. J.$\Delta$-sets. I. Homotopy theory.
Quart. J. Math. Oxford Ser. (2) 22 (1971), 321–338.
It is shown there that a Kan "semi-simpli …
- 18.5k
7
votes
Is every connected space equivalent to some B(Aut(X))?
If you are willing to relax your wish from having answer of the form $\text{Aut}(X)$
to the more general group-like
topological monoid $\text{Aut}_B(E)$ for a suitable fibration $E \to B$, then the a …
- 18.5k
7
votes
Homotopy equivalence of geometric realizations
Yes. If you are given a simplicial set $X: \Delta^{\text{op}} \to \text{Sets}$, then
the the thick realization $||X||$ of $X$ is given by the same formula as the ordinary realization with the excepti …
- 18.5k
1
vote
(Co)homological characterization of homotopy pullbacks
Here are some comments in the form of an answer, which can be viewed as the Koszul dual to Tyler's approach via the Eilenberg-Moore spectral sequence.
Firstly, in the special case when $D$ is a poin …
- 18.5k