Last Updated：2025/11/21
(mathematics) The property of there being a unique morphism from an arbitrary object to the universal morphism of a comma category which is from a functor to a fixed object; or, dually, the property of there being a unique morphism from the universal morphism to an arbitrary object of a comma category which is from a fixed object to a functor. (Caveat: the uniqueness is up to isomorphism.)
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universal property
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Source Word
universal property
Noun
(mathematics)
The
property
of
there
being
a
unique
morphism
from
an
arbitrary
object
to
the
universal
morphism
of
a
comma
category
which
is
from
a
functor
to
a
fixed
object;
or,
dually,
the
property
of
there
being
a
unique
morphism
from
the
universal
morphism
to
an
arbitrary
object
of
a
comma
category
which
is
from
a
fixed
object
to
a
functor.
(Caveat:
the
uniqueness
is
up
to
isomorphism.)
Japanese Meaning
数学、特に圏論における概念で、合同圏の文脈で定義される。具体的には、固定された対象と関手との間、またはその逆の関係において、普遍射（ユニヴァーサルモルフィズム）から任意の対象へ、または任意の対象から普遍射へ、一意（同型を許す一意）な射が存在するという性質を指す。
Sense（1）
(mathematics)
The
property
of
there
being
a
unique
morphism
from
an
arbitrary
object
to
the
universal
morphism
of
a
comma
category
which
is
from
a
functor
to
a
fixed
object;
or,
dually,
the
property
of
there
being
a
unique
morphism
from
the
universal
morphism
to
an
arbitrary
object
of
a
comma
category
which
is
from
a
fixed
object
to
a
functor.
(Caveat:
the
uniqueness
is
up
to
isomorphism.)
（ plural ）
