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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.

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Quillen equivalence, fibrant objects

Suppose that $G:M\leftrightarrow N: U$ is a Quillen equivalence between two model categories. Suppose that $a\in M$ is a fibrant object, is it true that there exists always a fibrant object $b\in N$ …
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