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 recent results of [23, 24, 25] as particular instances. And we also find new abelian model structures both in C(R) and in C(ωco(X)) attained to classes which are non necessarily closed under direct limits.
Original language | English |
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Pages (from-to) | 43-61 |
Number of pages | 19 |
Journal | Houston Journal of Mathematics |
Volume | 40 |
Issue number | 1 |
State | Published - Jan 1 2014 |
Keywords
- Complete cotorsion pair
- Homotopy category
- Model structure
- Cotorsion pairs
- Homotopy categories
- Model structures
DC Disciplines
- Education
- Mathematics