Fibrant model structures on weakly idempotent complete additive categories are equivalent to fibrantly weak factorization systems, and the homotopy category is the additive quotient of bifibrant objects by trivial bifibrant objects.
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Homotopy categories and fibrant model structures
Fibrant model structures on weakly idempotent complete additive categories are equivalent to fibrantly weak factorization systems, and the homotopy category is the additive quotient of bifibrant objects by trivial bifibrant objects.