On lifting stable diagrams in Frobenius categories

Details On lifting stable diagrams in Frobenius categories On lifting stable diagrams in Frobenius categories

2005-09-03

arxiv.org/abs/math/0509056v3

Mathematics

Category Theory

Added discussion of the connection to related work of Cooke, Dwyer-Kan-Smith and Mitchell. To appear in Homology, Homotopy and

Scientific paper

Suppose given a Frobenius category E, i.e. an exact category with a big enough subcategory B of bijectives. Let_E_ := E/B denote its classical stable category. For example, we may take E to be the category of complexes C(A) with entries in an additive category A, in which case_E_ is the homotopy category of complexes K(A). Suppose given a finite poset D that satisfies the combinatorial condition of being ind-flat. Then, given a diagram of shape D with values in_E_ (i.e. commutative up to homotopy), there exists a diagram consisting of pure monomorphisms with values in E (i.e. commutative) that is isomorphic, as a diagram with values in_E_, to the given diagram.

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