Last Updated：2025/12/31
Sentence
Given
a
pair
of
functors
S:𝒜→𝒞
and
T:ℬ→𝒞,
objects
of
the
comma
category
S↓T
are
arrows
h:S(A)→T(B)
parametrized
by
triples
(A,
B,
h),
and
given
morphisms
f:A→A'
and
g:B→B',
then
a
morphism
of
the
said
comma
category
is
a
commuting
square
parametrized
by
the
pair
(f,
g)
and
spanning
the
area
from
h
to
h':S(A')→T(B')
and
from
S(f)
to
T(g).
Quizzes for review
Given a pair of functors S:𝒜→𝒞 and T:ℬ→𝒞, objects of the comma category S↓T are arrows h:S(A)→T(B) parametrized by triples (A, B, h), and given morphisms f:A→A' and g:B→B', then a morphism of the said comma category is a commuting square parametrized by the pair (f, g) and spanning the area from h to h':S(A')→T(B') and from S(f) to T(g).
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