2024/01/12 by Kelly, Jack
#Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2401.06679
We develop techniques for constructing model structures on chain complexes valued in accessible exact categories, and apply this to show that for a closed symmetric monoidal, locally presentable exact category \mathpzcE with exact filtered colimits and enough flat objects, the flat cotorsion pair on \mathpzcE induces an exact model structure on Ch(\mathpzcE). Further we show that when enriched over ℚ such categories furnish convenient settings for homotopical algebra - in particular that they are Homotopical Algebra Contexts, and admit powerful Koszul duality theorems. As an example, we consider categories of sheaves valued in monoidal locally presentable exact categories.