Title

Cotorsion Pairs, Model Structures and Adjoints in Homotopy Categories

Document Type

Article

Publication Date

2014

Publication Title

Houston Journal of Mathematics

ISSN

0362-1588

Abstract

We will show the interlacing between complete cotorsion pairs, model structures and homotopy categories. This will give a method of constructing adjoint functors between homotopy categories as well as a method for constructing abelian model structures in the category of unbounded complexes of certain abelian categories. We illustrate our methods by recovering some recents results of Murfet and Neeman as particular instances. And we also find new abelian model structures both in C(R) and in C(Qco(X)) attained to classes which are non necessarily closed under direct limits.

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