The Prefix κατα- (“utterly / down”)

κατα- has two faces. As an INTENSIFIER it means “utterly, completely” and stacks onto an adjective or verb to crank it to the maximum: κουρασμένος (“tired”) → κατακουρασμένος (“dead tired, worn out”). This intensive κατα- is the productive one - it says “to the utmost”. Its older, LEXICALISED meaning is “down / against”, now frozen inside verbs you already know rather than freely added: κατεβαίνω (“I go DOWN, descend”) - the mirror of ανεβαίνω (“I go up”) - carries κατα- (“down”) fused into its root. So when you meet κατα-, weigh the two readings: on a fresh adjective it is almost always the intensive “utterly” (κατακουρασμένος = “utterly tired”); inside a fixed verb like κατεβαίνω it is the frozen “down”. Stress falls on the base word’s syllable (κατακουρασμένος, like κουρασμένος); κατα- itself is unstressed.