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Results tagged with simplicial-stuff
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user 123731
For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
8
votes
1
answer
884
views
Is totalization (of a cosimplicial category) a part of some adjunction?
For a diagram category $\Gamma$ and and a cocomplete category $\mathcal{C}$, we have an equivalence $$\mathrm{Fun}(\Gamma,\mathcal{C}) \simeq \mathrm{Adj}(Set^{\Gamma^{Op}},C)$$ where for $F: \Gamma \ …
- 765
6
votes
0
answers
134
views
Any comparison between the category of cubes and its opposite?
To model topological spaces combinatorially, one can use simplicial sets -- or cubical sets. Simplicial sets are defined as presheaves on the simplex category $\Delta$, the category of non-empty finit …
- 765
6
votes
1
answer
288
views
How are simplicial sets with Quillen model structure a simplicial model category?
I got very lost in checking that simplicial sets with Quillen model structure are indeed a simplicial model category.
Recall that a model category $\mathcal{M}$ is simplicial if it is enriched in $\ …
- 765
1
vote
0
answers
111
views
Based loops objects in model categories
If I have a pointed model category then for I can define based loops objects as homotopy pullbacks:
$\require{AMScd}$
\begin{CD}
\Omega X @>>> *\\
@V V V @VV V\\
* @>>> X
\end{CD}
If m …
- 765