On lifting stable diagrams in Frobenius categories

2005/09/03 by Matthias Kuenzer, Kuenzer, Matthias
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:18E10

paper · pdf · doi:10.48550/arxiv.math/0509056

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

arxiv created 2006/11/06 · arxiv updated 2009/12/01

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.

Related

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