group object

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|category theory}} Given a [[category]] ''C'', any [[object]] ''X ∈ C'' on which [[morphism]]s are defined corresponding to the [[group theory|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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