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Homotopy limits in type theory

Published online by Cambridge University Press:  19 January 2015

JEREMY AVIGAD ,
KRZYSZTOF KAPULKIN  and
PETER LEFANU LUMSDAINE
JEREMY AVIGAD
Affiliation:
Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A. Email: avigad@cmu.edu
KRZYSZTOF KAPULKIN
Affiliation:
Department of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A. E-mail: k.kapulkin@gmail.com
PETER LEFANU LUMSDAINE
Affiliation:
Institute for Advanced Study, Princeton, New Jersey, U.S.A. Email: p.l.lumsdaine@gmail.com
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Abstract

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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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