Last Updated：2026/01/01
Sentence
3.1.10
Example
If
you
forget
[that]
you
can
compose
arrows
in
a
category
and
you
forget
which
arrows
are
the
identities,
then
you
have
remembered
only
that
the
category
is
a
graph.
This
gives
an
underlying
functor
U:
mathbf
Cat→
mathbf
Grf,
since
every
functor
is
a
graph
homomorphism
although
not
vice
versa.
Quizzes for review
3.1.10 Example If you forget [that] you can compose arrows in a category and you forget which arrows are the identities, then you have remembered only that the category is a graph. This gives an underlying functor U: mathbf Cat→ mathbf Grf, since every functor is a graph homomorphism although not vice versa.
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