Homology and homotopy for arbitrary categories

One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was discovered with the development of Homology theory. Some of the deepest results in topology are about the connections between Homotopy and Homology. These results are proved using intricate constructions. This paper takes an axiomatic approach that provides a common ground for homotopy and homology in arbitrary categories. The axioms have simple and natural motivations, and lead to the deeper connections between homotopy and homology.