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Homotopy limits in type theory
Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A..ORCID iD: 0000-0002-4602-9779
Department of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A..
Institute for Advanced Study, Princeton, New Jersey, U.S.A..ORCID iD: 0000-0003-1390-2970
2015 (English)In: Mathematical Structures in Computer Science, ISSN 0960-1295, E-ISSN 1469-8072, Vol. 25, no 5, 1040-1070 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 25, no 5, 1040-1070 p.
Keyword [en]
homotopy type theory, homotopy limits, pullbacks, formalisation, proof assistants
National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-128394DOI: 10.1017/S0960129514000498OAI: oai:DiVA.org:su-128394DiVA: diva2:914763
Available from: 2016-03-25 Created: 2016-03-25 Last updated: 2016-04-04Bibliographically approved

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Publisher's full textarXiv:1304.0860

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Avigad, JeremyLumsdaine, Peter LeFanu
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