category

noun

Etymology: Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Indo-European *ḱm̥-th₂der.? Proto-Hellenic *kətá Ancient Greek κᾰτᾰ́ (kătắ) Ancient Greek κᾰτᾰ- (kătă-) Proto-Indo-European *h₂ger- Proto-Indo-European *h₂goréh₂ Proto-Hellenic *agorā́ Ancient Greek ἀγορᾱ́ (agorā́) Ancient Greek -εύς (-eús) Ancient Greek -εύω (-eúō) Ancient Greek ἀγορεύω (agoreúō) Ancient Greek κᾰτήγορος (kătḗgoros) Proto-Indo-European *-eti Proto-Indo-European *-eyéti Proto-Indo-European *-esyéti Proto-Indo-European *-éh₁ti Proto-Indo-European *-yeti Proto-Indo-European *-éh₁yeti Proto-Indo-European *-yeti Proto-Indo-European *-éyeti Ancient Greek -έω (-éō) Ancient Greek κᾰτηγορέω (kătēgoréō) Proto-Indo-European *-h₂ Proto-Indo-European *-éh₂ Proto-Indo-European *-i-eh₂ Proto-Hellenic *-íā Ancient Greek -ῐ́ᾱ (-ĭ́ā) Ancient Greek κᾰτηγορῐ́ᾱ (kătēgorĭ́ā)bor. Late Latin catēgoriader. Middle French categorie French catégoriebor. Middle English English category Late Middle English, borrowed from French catégorie, from Middle French categorie, from Late Latin catēgoria (“class of predicables”), from Ancient Greek κατηγορία (katēgoría, “head of predicables”). Doublet of categoria.

1. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.

   “This steep and dangerous climb belongs to the most difficult category.”

   “I wouldn’t put this book in the same category as the author’s first novel.”

2. A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.

   “One well-known category has sets as objects and functions as arrows.”

   “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.”