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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.

6 votes
0 answers
241 views

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 …
Rene Recktenwald's user avatar
1 vote
1 answer
222 views

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 …
Rene Recktenwald's user avatar
1 vote
0 answers
99 views

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 …
Rene Recktenwald's user avatar