Kapulkin, K and Szumilo, K (2019) Internal Languages of Finitely Complete (∞, 1)-categories. Selecta Mathematica, 25. 33. ISSN 1022-1824
Abstract
We prove that the homotopy theory of Joyal’s tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-Löf Type Theory with dependent sums and intensional identity types is the internal language of (∞, 1)-categories with finite limits.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2019. This is a post-peer-review, pre-copyedit version of an article published in Selecta Mathematica. The final authenticated version is available online at: https://doi.org/10.1007/s00029-019-0480-0. |
Keywords: | type theory; homotopy theory; higher category theory; 18G55; 55U35; 03B15 (primary) |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jun 2019 09:35 |
Last Modified: | 27 Apr 2020 00:40 |
Status: | Published |
Publisher: | Springer International Publishing |
Identification Number: | 10.1007/s00029-019-0480-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147370 |