Last Updated：2026/01/01
Sentence
If
H
is
another
group
object
in
C,
a
morphism
f:G→H
is
a
morphism
of
group
objects
if
it
commutes
with
the
three
structure
morphisms;
as
is
standard
for
sets
and
true
generally
(again
by
Lemma
7.7),
it
is
enough
to
check
𝜇.
Thus
we
form
the
category
textit
Gp(C)
of
all
group
objects
in
C;
one
important
example
is
textit
Gp(
textit
Ho).
Quizzes for review
If H is another group object in C, a morphism f:G→H is a morphism of group objects if it commutes with the three structure morphisms; as is standard for sets and true generally (again by Lemma 7.7), it is enough to check 𝜇. Thus we form the category textit Gp(C) of all group objects in C; one important example is textit Gp( textit Ho).
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