Delta functor

Summary

A delta functor, or $\delta$-functor, is a sequence of additive functors $T^0, T^1, T^2, \dots$ between abelian categories, together with connecting maps. These turn each short exact sequence into a long exact sequence. It is the axiomatic form of a cohomology theory. The right derived functors of a left exact functor form a universal $\delta$-functor, and universality is how one recognizes derived functors without resolutions.