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Results tagged with model-categories
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user 22989
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.
10
votes
When is a functor a right derived functor?
Here's a counterexample for unbounded derived categories (this doesn't answer the revised question with the "$t$-left exact" condition).
Suppose $\mathcal{A}$ is a Grothendieck category with enough p …
- 35.2k
20
votes
Accepted
Is the homotopy category of an abelian model category abelian?
No. The projective model structure on chain complexes of modules over a ring is an abelian model category, and the homotopy category is the derived category, which is never abelian unless the ring is …
- 35.2k
7
votes
Accepted
Split cofibrations up to quasi-isomorphism
No. You can construct counterexamples by taking projective resolutions of modules in a nonsplit short exact sequence. For example, from the short exact sequence $0\to\mathbb{Z}\stackrel{2}{\to}\mathbb …
- 35.2k