Homotopy limits in type theory

2 Apr 2013 · Jeremy Avigad, Chris Kapulkin, Peter LeFanu Lumsdaine ·

Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.