Last Updated
：2025/12/05
free category
Noun
(category
theory)
A
category
that
is
induced
by
a
multidigraph
thus:
it
has
as
its
objects
the
vertices
of
the
multidigraph
and
its
morphisms
are
paths
in
the
multidigraph;
composition
of
morphisms
is
concatenation
of
paths,
as
long
as
the
end
of
one
path
coincides
with
the
beginning
of
the
other
path;
an
identity
morphism
of
an
object
is
an
“empty
path”
at
that
vertex.
Japanese Meaning
フリー圏（カテゴリー理論における）: 多重有向グラフから誘導される圏であり、オブジェクトがグラフの頂点、射が頂点間の経路で定義される。射の合成は、ある経路の終点と他の経路の始点が一致する場合、それらの経路を連結することで実現され、各オブジェクトにおける恒等射は空の経路として表される。
Sense（1）
(category
theory)
A
category
that
is
induced
by
a
multidigraph
thus:
it
has
as
its
objects
the
vertices
of
the
multidigraph
and
its
morphisms
are
paths
in
the
multidigraph;
composition
of
morphisms
is
concatenation
of
paths,
as
long
as
the
end
of
one
path
coincides
with
the
beginning
of
the
other
path;
an
identity
morphism
of
an
object
is
an
“empty
path”
at
that
vertex.
（ plural ）
Quizzes for review
(category theory) A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex.
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See correct answer
free category
To illustrate composition of morphisms, we construct the free category on the given multidigraph and trace each path as a morphism.
See correct answer
To illustrate composition of morphisms, we construct the free category on the given multidigraph and trace each path as a morphism.
音声機能が動作しない場合はこちらをご確認ください
English - English
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