Dexter Kozen, Christoph Kreitz, and Eva Richter. Automating proofs in category theory. In: Proc. 3rd Int. Joint Conf. Automated Reasoning (IJCAR'06), number 4130 in Lecture Notes in AI, pages 392-407. Springer, August 2006.

We introduce a semi-automated proof system for basic category-theoretic reasoning. It is based on a first-order sequent calculus that captures the basic properties of categories, functors and natural transformations as well as a small set of proof tactics that automate proof search in this calculus. We demonstrate our approach by automating the proof that the functor categories Fun[CxD,E] and Fun[C,Fun[D,E]] are naturally isomorphic.