We introduce a new CCG parsing model which is factored on lexical category assignments. Parsing is then simply a deterministic search for the most probable category sequence that supports a CCG derivation. The parser is extremely simple, with a tiny feature set, no POS tagger, and no statistical model of the derivation or dependencies. Formulating the model in this way allows a highly effective heuristic for A * parsing, which makes parsing extremely fast. Compared to the standard C&C CCG parser, our model is more accurate out-of-domain, is four times faster, has higher coverage, and is greatly simplified. We also show that using our parser improves the performance of a state-ofthe-art question answering system.