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Results tagged with model-categories
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user 360
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.
15
votes
1
answer
967
views
When is the category of pro-objects a homotopy category?
For a category $C$, there is a category Pro-$C$ whose objects are cofiltered diagrams $I \to C$ and whose morphisms are given by
$$
{\rm Hom}(\{x_s\},\{y_t\}) = \varprojlim_t\ \varinjlim_s\ {\rm Hom}( …
- 52.6k
25
votes
4
answers
4k
views
How canonical is cofibrant replacement?
Quillen's original definition of a model category included noncanonical factorization axioms, one being that any map can be factored into a cofibration followed by an acyclic fibration. More recent r …
- 52.6k
7
votes
1
answer
918
views
Is there a cheap proof that (homotopy) endomorphisms are functorial?
This is, in some sense, the homotopy version of this question.)
If $C$ is a category with $iC$ the subcategory of isomorphisms, there is a functor $X \mapsto End(X)$ from $iC$ to the category of mono …
- 52.6k