Awodey, S, Gambino, N orcid.org/0000-0002-4257-3590 and Sojakova, K (2017) Homotopy-initial algebras in type theory. Journal of the ACM, 63 (6). ISSN 1535-9921
Abstract
We investigate inductive types in type theory, using the insights provided by homotopy type theory and univalent foundations of mathematics. We do so by introducing the new notion of a homotopy-initial algebra. This notion is defined by a purely type-theoretic contractibility condition which replaces the standard, category-theoretic universal property involving the existence and uniqueness of appropriate morphisms. Our main result characterises the types that are equivalent to W-types as homotopy-initial algebras.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Journal of the ACM, (Vol:63, Iss 6, (Feb 2017) https://doi.org/10.1145/3006383 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number John Templeton Foundation - DO NOT USE 48138 EPSRC (Engineering and Physical Sciences Research Council) EP/M01729X/1 Air Force Research Lab Munitions Directorate FA8655-13-1-3038, 12.800 |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Oct 2016 09:35 |
Last Modified: | 16 Mar 2020 12:30 |
Published Version: | https://doi.org/10.1145/3006383 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Identification Number: | 10.1145/3006383 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:105765 |