Notes on several orthogonal classes of flat and FP-injective functors

Abstract

In this paper, we develop relative homological algebra in the category of functors from finitely presented modules to Abelian groups. More specifically, we introduce the concepts of \(\mathfrak{F}\)-injective, \(\mathfrak{F}\)-projective and \(\mathfrak{F}\)-flat functors. Such functors appear when we study covers and envelopes of functors. The relationships among these functors are investigated and some applications are given.