Source Word
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 ）
