1580s, in Aristotle's logic, "a highest notion," from French catégorie, from Late Latin categoria, from Greek kategoria "accusation, prediction, category," verbal noun from kategorein "to speak against; to accuse, assert, predicate," from kata "down to" (or perhaps "against;" see cata-) + agoreuein "to harangue, to declaim (in the assembly)," from agora "public assembly" (from PIE root *ger- "to gather").
The verb's original sense of "accuse" had weakened to "assert, name" by the time Aristotle applied kategoria to his 10 classes of things that can be named. Exactly what he meant by it "has been disputed almost from his own day till the present" [OED]. Sense of "any very wide and distinctive class, any comprehensive class of persons or things" is from 1660s.
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]
Proto-Indo-European root meaning "to gather."
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit gramah "heap, troop;" Greek ageirein "to assemble," agora "assembly;" Latin grex "flock, herd," gremium "bosom, lap;" Old Church Slavonic grusti "handful," gramota "heap;" Lithuanian gurgulys "chaos, confusion," gurguolė "crowd, mass;" Old English crammian "press something into something else."
late 15c., "to distribute into groups or classes," from Old French assorter "to assort, match" (15c., Modern French assortir), from a- "to" (see ad-) + sorte "kind, category," from Latin sortem (nominative sors) "lot; fate, destiny; share, portion; rank, category; sex, class, oracular response, prophecy" (from PIE root *ser- (2) "to line up"). Related: Assorted; assorting.
early 15c., in philosophy, "category, class; one of Aristotle's 10 categories," from Medieval Latin predicamentum, from Late Latin praedicamentum "quality, category, something predicted, that which is asserted," from Latin praedicatus, past participle of praedicare "assert, proclaim, declare publicly," from prae- "forth, before" (see pre-) + dicare "proclaim" (from PIE root *deik- "to show," also "pronounce solemnly," and see diction). Praedicamentum is a loan-translation of Greek kategoria, Aristotle's word.
The meaning "unpleasant, dangerous, or trying situation" is a particular negative use of the general sense of "a state of being, condition, situation" (1580s).