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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.
7
votes
Why do we need model categories?
Extensive answers have already been given in this thread. Just a few remarks here and there.
I think the question “why we need” assumes something about “we”, and in some extent, about “need”. There …
5
votes
Derivators and fibred $\infty$-categories
I am no Denis-Charles but given the other paper you quoted let me think of a sketch, perhaps you will be able to make the right out of it.
Let $\mathcal E \to \mathcal C$ be a Quillen presheaf (model …
1
vote
Deriving the functor $ \int_{\Gamma} F(-,-)$
A long comment.
The way you state the question currently mixes the abstract notion of derived functor (has nothing to do with fibrant replacements), and the notion of a co/fibrant replacement. I am …