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Chen, Joshua (2025) Internal constructions in homotopical type theory. PhD thesis, University of Nottingham.

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Abstract

The aim of this thesis is to investigate certain constructions that resist satisfactory full internalizations in plain homotopy type theory, i.e. intensional Martin-Löf type theory with the univalence axiom.

In Part I, we study internal higher categorical models of homotopical type theory, via wild categories with families (cwfs). We formulate coherence conditions on wild cwfs that suffice to recover properties expected of models of dependent type theory. The result is a definition of a 2-coherent wild cwf, which admits as instances both the syntax and the "standard model" given by a universe type. We also identify a higher "splitness" coherence condition that is satisfied by all set-level cwfs and univalent 2-coherent wild cwfs.

In Part II, we apply some of the theory developed in Part I and report on a partial investigation into the construction of type-valued Reedy-fibrant inverse diagrams in plain HoTT.

Item Type:	Thesis (University of Nottingham only) (PhD)
Supervisors:	Kraus, Nicolai
Keywords:	homotopical type theory, homotopy type theory, HoTT
Subjects:	Q Science > QA Mathematics > QA 75 Electronic computers. Computer science
Faculties/Schools:	UK Campuses > Faculty of Science > School of Computer Science
Item ID:	81663
Depositing User:	Chen, Joshua
Date Deposited:	31 Dec 2025 04:40
Last Modified:	31 Dec 2025 04:40
URI:	https://eprints.nottingham.ac.uk/id/eprint/81663

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