# Homotopy limits in type theory

@article{Avigad2015HomotopyLI,
title={Homotopy limits in type theory},
author={Jeremy Avigad and Krzysztof Kapulkin and Peter LeFanu Lumsdaine},
journal={Mathematical Structures in Computer Science},
year={2015},
volume={25},
pages={1040 - 1070}
}
• Published 2 April 2013
• Mathematics
• 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.

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