A GENERALIZATION OF HOMOLOGICAL ALGEBRA Davvaz, B.; Shabani-Solt, H.;
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 -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.