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Additional
abelian category
English Wikipedia - The Free Encyclopedia
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Abelian category
In
mathematics
, an
abelian category
is a
category
in which
morphisms
and objects can be added and in which
kernel
s and
cokernels
exist and have desirable properties. The motivating prototype example of an abelian category is the
category of abelian groups
,
Ab
. The theory originated in an effort to unify several
cohomology theories
by
Alexander Grothendieck
and independently in the slightly earlier work of
David Buchsbaum
. Abelian categories are very
stable
categories, for example they are
regular
and they satisfy the
snake lemma
. The class of Abelian categories is closed under several categorical constructions, for example, the category of
chain complexes
of an Abelian category, or the category of
functors
from a
small category
to an Abelian category are Abelian as well. These stability properties make them inevitable in
homological algebra
and beyond; the theory has major applications in
algebraic geometry
,
cohomology
and pure
category theory
. Abelian categories are named for
Niels Henrik Abel
.
See more at Wikipedia.org...
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