Homotopy limits in type theory

JEREMY AVIGAD, KRZYSZTOF KAPULKIN, PETER LEFANU LUMSDAINE
2015 Mathematical Structures in Computer Science  
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 the formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.
doi:10.1017/s0960129514000498 fatcat:h72zjn2fknduzls36hsw5mkvqu