Geodesic
On lifting stable diagrams in Frobenius categories
Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 163-183.

Voir la notice de l'article provenant de la source International Press of Boston

Suppose given a Frobenius category ${\cal E}$, i.e. an exact category with a big enough subcategory ${\cal B}$ of bijectives. Let $\underline{\cal E} := {\cal E}/{\cal B}$ denote its classical stable category. For example, we may take ${\cal E}$ to be the category of complexes $\mathrm{C}({\cal A})$ with entries in an additive category ${\cal A}$, in which case $\underline{\cal E}$ is the homotopy category of complexes $\mathrm{K}({\cal A})$. 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 $\underline{\cal E}$ (i.e. stably commutative), there exists a diagram consisting of pure monomorphisms with values in ${\cal E}$ (i.e. commutative) that is isomorphic, as a diagram with values in $\underline{\cal E}$, to the given diagram.
DOI : 10.4310/HHA.2007.v9.n1.a6
Classification : 18E10
Keywords: Stable Frobenius category 
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Matthias Künzer. On lifting stable diagrams in Frobenius categories. Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 163-183. doi : 10.4310/HHA.2007.v9.n1.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n1.a6/

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