Automating proofs in category theory

Authors:
Dexter Kozen;Christoph Kreitz;Eva Richter
Affiliations:
Computer Science Department, Cornell University, Ithaca, NY;,Computer Science Department, Cornell University, Ithaca, NY;Institut für Informatik, Universität Potsdam, Potsdam, Germany
Venue:
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Year:
2006

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Abstract

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[C×D, E] and Fun[C, Fun[D, E] ] are naturally isomorphic.