A Model Of Type Theory In Cubical Sets With Connections
Simon Docherty
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.