MoL-2014-12: A Model Of Type Theory In Cubical Sets With Connections

MoL-2014-12: Docherty, Simon (2014) A Model Of Type Theory In Cubical Sets With Connections. [Report]

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Abstract

In this thesis we construct a new model of intensional type theory in the category of cubical sets with connections. To facilitate this we introduce the notion of a nice path object category, a simplification of the path object category axioms of v.d. Berg and Garner that nonetheless yields the full path object category structure. By defining cubical n-paths and contraction operators upon them we exhibit the category of cubical sets with connections as a nice path object category, and are therefore able to utilise a general construction of a homotopy theoretic model of identity types from the structure of a path object category in order to give our model of type theory.

Item Type: Report
Report Nr: MoL-2014-12
Series Name: Master of Logic Thesis (MoL) Series
Year: 2014
Uncontrolled Keywords: logic, mathematics
Subjects: Logic
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/930

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