Model categories have been an important tool in algebraic topology since rst de ned by Quillen. Given a category and a class of morphisms called weak equivalences one can study the homotopy \category" in which the weak equivalences are turned into isomorphisms by formally giving them inverses. However, the resulting structure might not be a category, and even when it is understanding it can be very di cult. A model structure on a category ensures that formally inverting the weak equivalence...[Show more]
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