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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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The homotopy category of the category of enriched categories

There's a different obstacle; the change-of-enrichment functor $\mathsf{Cat}_{\mathcal C} \to \mathsf{Cat}_{\operatorname{Ho}\mathcal C}$ doesn't invert the weak equivalences! Instead, this is a relat …
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