Category Of Groups
In
mathematics
, the
category
Grp
has the
class
of all
groups
for objects and
group homomorphisms
for
morphisms
. As such, it is a
concrete category
. The study of this category is known as
group theory
. The category
Grp
is both
complete and co-complete
. The
product
is just the
direct product
while the
coproduct
is the
free product
. The
zero objects
in
Grp
are the
trivial groups
(consisting of just an identity element). The
category of abelian groups
,
Ab
, is a
full subcategory
of
Grp
.
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