A generalization of homological algebra

Abstract

Our aim in this paper is to introduce a generalization of some notions in homological algebra,. We define the concepts of chain U-complex, U-homology, chain (U, U′)-map, chain (U, U′)-homotopy and U-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.