(also nonabelian homological algebra)
Context
Basic definitions
Stable homotopy theory notions
Constructions
Lemmas
Homology theories
Theorems
additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
Let , be two abelian categories.
A homological -functor from to is for each a functor
equipped for each short exact sequence in with a natural transformation
such that for each such short exact sequence there is, naturally a long exact sequence
The archetypical example is the chain homology functor
from the category of chain complexes of some abelian category (for -graded complexes).
The universal example are (non-total) right derived functors.
The notion is due to
A textbook account is for instance section 2.1 of
Last revised on September 30, 2017 at 00:00:16. See the history of this page for a list of all contributions to it.