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Let be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs $(, \tilde{})$ and $(\tilde{},)$ in satisfying $\tilde{} \subseteq$ and $\cap \tilde{} = \tilde{} \cap$ . We show how to construct a (necessarily unique) abelian model structure on with (resp. $\tilde{}$ ) as the class of cofibrant (resp. trivially cofibrant) objects, and (resp. $\tilde{}$ ) as the class of fibrant (resp. trivially fibrant) objects.

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Homotopy equivalence of isospectral graphs.

Homotopy groups of small categories and derived functors

Homotopy Inverses for Nerve.

Homotopy limits in triangulated categories

Homotopy theory for (braided) cat-groups

Homotopy-theoretic aspects of 2-monads.

How to construct a Hovey triple from two cotorsion pairs

Currently displaying 41 – 47 of 47