Matrix factorizations for self-orthogonal categories of modules
Peer reviewed, Journal article
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OriginalversjonJournal of Algebra and its Applications. 2020, . 10.1142/S0219498821500377
For a commutative ring S and self-orthogonal subcategory C of Mod(S), we consider matrix factorizations whose modules belong to C. Let f∈S be a regular element. If f is M-regular for every M∈C, we show there is a natural embedding of the homotopy category of C-factorizations of f into a corresponding homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence if C is the category of projective or flat-cotorsion S-modules. Dually, using divisibility in place of regularity, we observe there is a parallel equivalence when C is the category of injective S-modules.