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Results tagged with model-categories
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user 123731
A model category is a category equipped with notions of weak equivalences, fibrations and cofibrations allowing to run arguments similar to those of classical homotopy theory.
1
vote
0
answers
111
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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
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
7
votes
0
answers
143
views
DG functors along which contractions can be lifted
For an object $X$ in a DG category, its contraction is $r \in Hom^{-1}(X,X)$ such that $d(r)=1_X$. Let us say that contractions lift along a DG functor $F: \mathcal{C} \to \mathcal{D}$, if for a contr …
- 765