Last Updated
：2025/12/04
group object
Noun
(category
theory)
Given
a
category
C,
any
object
X
∈
C
on
which
morphisms
are
defined
corresponding
to
the
group
theoretic
concepts
of
a
binary
operation
(called
multiplication),
identity
and
inverse,
such
that
multiplication
is
associative
and
properties
are
satisfied
that
correspond
to
the
existence
of
inverse
elements
and
the
identity
element.
Japanese Meaning
圏論において、与えられた圏Cの中の対象Xで、群論における二項演算（掛け算）、単位元、逆元に対応する射が定義され、これらの射が結合性や逆元、単位元の存在に対応する性質を満たすような対象を指す。
Sense（1）
(category
theory)
Given
a
category
C,
any
object
X
∈
C
on
which
morphisms
are
defined
corresponding
to
the
group
theoretic
concepts
of
a
binary
operation
(called
multiplication),
identity
and
inverse,
such
that
multiplication
is
associative
and
properties
are
satisfied
that
correspond
to
the
existence
of
inverse
elements
and
the
identity
element.
（ plural ）
Quizzes for review
(category theory) Given a category C, any object X ∈ C on which morphisms are defined corresponding to the group theoretic concepts of a binary operation (called multiplication), identity and inverse, such that multiplication is associative and properties are satisfied that correspond to the existence of inverse elements and the identity element.
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See correct answer
group object
In the category of schemes, a group object is an object X equipped with morphisms for multiplication, identity, and inverse that satisfy the group axioms.
See correct answer
In the category of schemes, a group object is an object X equipped with morphisms for multiplication, identity, and inverse that satisfy the group axioms.
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English - English
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