Previous CCG supertaggers usually predict categories using multi-class classification. Despite their simplicity, internal structures of categories are usually ignored. The rich semantics inside these structures may help us to better handle relations among categories and bring more robustness into existing supertaggers. In this work, we propose to generate categories rather than classify them: each category is decomposed into a sequence of smaller atomic tags, and the tagger aims to generate the correct sequence. We show that with this finer view on categories, annotations of different categories could be shared and interactions with sentence contexts could be enhanced. The proposed category generator is able to achieve state-of-the-art tagging (95.5% accuracy) and parsing (89.8% labeled F1) performances on the standard CCGBank . Further-more, its performances on infrequent (even unseen) categories, out-of-domain texts and low resource language give promising results on introducing generation models to the general CCG analyses.