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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.

12 votes

Categories which are not compactly generated

One example is the following - suppose that $M$ is a non-compact connected manifold of dimension $\geq 1$. Then the unbounded derived category of chain complexes of sheaves of abelian groups on $M$ ha …
Greg Stevenson's user avatar
5 votes

How to think about model categories?

One can also view model structures as a solution to the problem of when is a localization of a category locally small. In other words when one wants to invert a collection of morphisms the morphisms i …
Greg Stevenson's user avatar