group object

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(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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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.

詳細

意味（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.

If H is another group object in C, a morphism f:G→H is a morphism of group objects if it commutes with the three structure morphisms; as is standard for sets and true generally (again by Lemma 7.7), it is enough to check 𝜇. Thus we form the category textit Gp(C) of all group objects in C; one important example is textit Gp( textit Ho).

詳細

group objects （ plural ）