Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category

Abstract

We consider Lambek's invariants $\text{Ker}$ and $\text{Im}$ for commutative squares in Grandis homological categories. We prove that Nomura's null sequences exist in such categories and find sufficienct conditions for their exactness. We also prove the coincidence of left and right homology in Grandis homological categories.