Just as a monoid consists of an underlying set with a binary operation 'on top of it' which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation 'on top of it' which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid. Synonyms [ ] • ( group to which items are assigned ):,,,,,,,,, • See also Hyponyms [ ].
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