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2
votes
Does the stable category of a nice exact category embed in (the underlying category of) a de...
This is not exactly answering your question but: a Frobenius category $\mathcal{E}$ (with suitable assumptions) can be given the structure of a model category whose homotopy category is the stable cat …
4
votes
Accepted
Extension-closed subcategories of triangulated categories as "almost exact" categories
There is a beautiful paper by Iyama and Yoshino (http://arxiv.org/abs/math/0607736). The main result in Section 4 is closely related to your question. The authors consider some extension-closed subcat …