A homotopy theory of additive categories with suspensions
arXiv:1703.02809
Abstract
We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion pairs) in an arbitrary exact category. We show that the homotopy category of an exact model structure (in the sense of Hovey) in a weakly idempotent complete exact category is equivalent to the subfactor category of cofibrant-fibrant objects as pre-triangulated categories.
arXiv commentany comments are welcome. arXiv admin note: text overlap with arXiv:1510.02258
References in corpus (5)
- On exact categories and applications to triangulated adjoints and model structures
- Triangulated categories without models
- From triangulated categories to module categories via localisation II: Calculus of fractions
- The triangulation of the subfactor categories of additive categories with suspensions
- Frobenius condition on a pretriangulated category, and triangulation on the associated stable category