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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.

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 …
Edouard's user avatar
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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 …
Edouard's user avatar
  • 660
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 …
Edouard's user avatar
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