On lifting stable diagrams in Frobenius categories
Abstract
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.
Cite
@article{arxiv.math/0509056,
title = {On lifting stable diagrams in Frobenius categories},
author = {Matthias Kuenzer},
journal= {arXiv preprint arXiv:math/0509056},
year = {2007}
}
Comments
Added discussion of the connection to related work of Cooke, Dwyer-Kan-Smith and Mitchell. To appear in Homology, Homotopy and Applications