Homological Transfer between Additive Categories and Higher Differential Additive Categories

Given an additive category C and an integer n >= 2. The higher differential additive category consists of objects X in C equipped with an endomorphism epsilon(X) satisfying epsilon(n)(X) = 0. Let R be a finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(t(n))-modules. It is proved that a finitely generated left R-module M is tau-rigid (respectively, (support) tau-tilting, almost complete tau-tilting) if and only if so is T(M) as a left R[t]/(t(n))-module. Moreover, R is tau(m)-selfinjective if and only if so is R[t]/(t(n)).