Categorical matrix factorizations and monomorphism categories

This article generalizes the correspondence between matrix factorizations and maximal Cohen-Macaulay modules over hypersurface rings due to Eisenbud and Yoshino. We consider factorizations with several factors in a purely categorical context, extending results of Sun and Zhang for Gorenstein projective module factorizations. Our formulation relies on a notion of hypersurface category and replaces Gorenstein projectives by objects of general Frobenius exact subcategories. We show that factorizations over such categories form again a Frobenius category. Our main result is then a triangle equivalence between the stable category of factorizations and that of chains of monomorphisms.