(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
Let , be two abelian categories.
A homological -functor from to is for each a functor
The archetypical example is the chain homology functor
The universal example are (non-total) right derived functors.
The notion is due to
A textbook account is for instance section 2.1 of