word-forming element meaning "down, downward," but also "through, on, against, concerning," etc., from Latinized form of Greek kata-, before vowels kat-, from kata "down, downward, down from, down to," from PIE *kmt- "down, with, along" (source also of Hittite kattan (adv.) "below, underneath," katta "along with"). Occasionally in Greek it had senses of "against" (catapult) or "wrongly" (catachresis), also "along, through, over, across, concerning." Also sometimes used as an intensive or with a sense of completion of action (catalogue). Very active in ancient Greek, this prefix is found in English mostly in words borrowed through Latin after c. 1500.
before vowels, cephal-, word-forming element meaning "head, skull, brain," Modern Latin combining form of Greek kephalē "head, uppermost or top part, source," from PIE *ghebh-el- (source also of Tocharian spal "head;" Old High German gebal "skull;" also, via the notion of "front," Gothic gibla, Old Norse gafl "side of a facade").
word-forming element meaning "horn, horn-like part," from Latinized form of Greek keras (genitive keratos) "horn of an animal; horn as a substance," from PIE root *ker- (1) "horn, head."
word-forming element meaning "brain, of the brain and," from Latin cerebrum "the brain" (see cerebral).
word-forming element meaning "wax, waxy," from Latinized form of Greek kēros "beeswax," a word of unknown origin with no obvious ulterior connections. "As there is no evidence for Indo-European apiculture, we have to reckon with foreign origin for κηρός" [Beekes].
before vowels chaet-, word-forming element meaning "hair," also, in scientific use, "spine, bristle," from Latinized form of Greek khaite "long, loose, flowing hair" (of persons, also of horses, lions), from an old PIE word for "hair, mane," source also of Avestan gaesa- "curly hair," gaesu- "'curly haired," Modern Persian ges "hair that hangs down, curls;" Middle Irish gaiset "bristly hair."