1588, from M.Fr. catégorie, from L.L. categoria, from Gk. kategorein "to accuse, assert, predicate," from kata "down to," + agoreuein "to declaim (in the assembly)," from agora "public assembly." Original sense of "accuse" weakened to "assert, name" by the time Aristotle applied kategoria to his 10 classes of things that can be named. Categorize is attested from 1705; categorization is from 1886.
"category should be used by no-one who is not prepared to state (1) that he does not mean class, & (2) that he knows the difference between the two ...." [Fowler]