Last Updated
：2025/11/21
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 ）
Quizzes for review
(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.)
音声機能が動作しない場合はこちらをご確認ください
See correct answer
universal property
In category theory, a limit is characterized by its universal property, which guarantees a unique morphism from any other cone to the limiting cone.
See correct answer
In category theory, a limit is characterized by its universal property, which guarantees a unique morphism from any other cone to the limiting cone.
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
Word Edit Setting
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Sentence Edit Setting
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Quiz Edit Setting
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
