标题： 范畴矩阵分解和单态射范畴 显示英文标题

标题： Categorical matrix factorizations and monomorphism categories

摘要： 本文推广了Eisenbud和Yoshino关于矩阵因子化与超曲面环上的极大Cohen-Macaulay模之间的对应关系。 我们考虑在纯范畴背景下具有多个因子的因子化，扩展了Sun和Zhang关于Gorenstein投射模因子化的结果。 我们的表述依赖于超曲面范畴的概念，并用一般Frobenius正合子范畴中的对象替换了Gorenstein投射模。 我们证明了在这种范畴上的因子化再次形成一个Frobenius范畴。 我们的主要结果是因子化的稳定范畴与单调递增链的稳定范畴之间的一个三角等价。 显示英文摘要

摘要： 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.