Categories, abelian categories and cohomologies.

Yoshifumi Tsuchimoto

We refer to [1] for a good guide to the theory.

Main idea: Instead of dealing with an object of an additive category $\mathcal{C}$ , we deal with complexes of $\mathcal{C}$ . But:

1. We want to regard quasi-isomorphic complexes as the ``same''.
2. We want to identify two morphisms to be the same if they are homotopic.