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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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Flat Model Structure on $\mathbf{Ch}(\mathbf{Mod}(\mathcal{O}_X))$ computes pullback / pushf...
Given a ringed space $(X,\mathcal{O})$ of can construct the flat model structure on chain complexes of $\mathcal{O}$-modules:
Weak equivalences are quasi-isomorphisms
The fibrations are epimorphisms …
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What came of the problems posed in Hovey's book chapter 8
In his book "Model Categories", Hovey sets out to write a self-contained introduction to model categories. The final chapter briefly discusses some questions which stayed unresolved.
I have been wond …
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Clarification on definition of closed $\mathcal{C}$-module for a category $\mathcal{C}$
Hovey introduces the notion of a closed monoidal structure and a closed monoidal functor. Then he goes on to say that this naturally gives rise to the notion of closed modules over a closed monoidal c …