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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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When do colimits agree with homotopy colimits?

I'm wondering about when the colimit and the homotopy colimit agree with diagrams of simplicial sets. I know that hocolim$(F)=$colim$(F_c)$ where $F_c$ is the cofibrant replacement of $F$. However, it …
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