MoL-2021-02: Algebraic models of type theory

MoL-2021-02: van Woerkom, Wijnand Koen (2021) Algebraic models of type theory. [Report]

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In the seminal work by Awodey and Warren it was shown that the intensional identity types of Martin-Löf dependent type theory can be modelled categorically using weak factorisation systems. In this interpretation the dependent types are modelled by fibrations, i.e. the right maps of a weak factorisation system. This work inspired a lot of further research into such categorical models of identity types. Recently it was adapted by Gambino and Larrea to the setting of algebraic weak factorisation systems who added interpretations of the dependent sum and product types of said type theory. In their work the dependent types are interpreted using the algebras of the pointed endofunctor of the system, and in the present work we show that the same approach also works when we instead use the algebras for the monad of the system.

Item Type: Report
Report Nr: MoL-2021-02
Series Name: Master of Logic Thesis (MoL) Series
Year: 2021
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 25 Mar 2021 15:38
Last Modified: 25 Mar 2021 15:38

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