Directed Type Theory
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Talks
2024 EuroProofNet WG6 Meeting
Towards Modal SOGATs
— at the 2024 Meeting of the EuroProofNet Working Group 6, 04 April 2024, Leuven, Belgium
HoTT/UF 2024
A Sampling of Synthetic 1-Category Theory
— at the Workshop on Homotopy Type Theory/Univalent Foundations, 03 April 2024, Leuven, Belgium
ASSUME
The Γ-Cube: Polarities and Modalities
— at the February 2024 meeting of ASSUME, 01 February 2024, Birmingham, UK
I discuss the interrelationships of eight standard models of dependent type theory, which are defined in a uniform way from eight categories of structures: sets, setoids, (univalent) groupoids, posets, preorders, and (univalent) categories. In particular, I highlight the 'negation' and 'core' modalities which exist on the latter four models, arising from their relationship to the former four. I also describe how this system of polarity sets the stage for semantics of directed type theory. Joint work with Thorsten Altenkirch.
HoTT 2023
Presheaf Models of Polarized Higher-Order Abstract Syntax
— at the Second International Conference on Homotopy Type Theory, 24 May 2023, Pittsburgh, USAThe Gamma Cube
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Party Like It's 1999
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Directed HOAS and Beyond
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HoTT/UF 2023
The Category Interpretation of (Polarized and Directed) Type Theory
— at the Workshop on Homotopy Type Theory/Univalent Foundations, 23 April 2023, Vienna, AustriaOntological Scandal!
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Replace Groupoids with Categories
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A Vision of Directed J
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HoTT/UF 2022
Towards Directed Higher Observational Type Theory
— at the Workshop on Homotopy Type Theory/Univalent Foundations, 01 August 2022, Haifa, IsraelThe Category Interpretation of Type Theory
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A Dream of Directed HOTT
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