A homotopy theory of additive categories with suspensions Article Swipe

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Mathematics Homotopy category Cofibration Homotopy Model category Pure mathematics Concrete category Higher category theory Regular homotopy Homotopy hypothesis n-connected 2-category Closed category Homotopy sphere Algebra over a field Functor

Zhiwei Li ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1703.02809 · OA: W2464905729

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.