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arXiv · 1602.08206

Fibred Fibration Categories

Taichi Uemura
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Abstract

We introduce fibred type-theoretic fibration categories which are fibred categories between categorical models of Martin-L\"{o}f type theory. Fibred type-theoretic fibration categories give a categorical description of logical predicates for identity types. As an application, we show a relational parametricity result for homotopy type theory. As a corollary, it follows that every closed term of type of polymorphic endofunctions on a loop space is homotopic to some iterated concatenation of a loop.

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Taichi Uemura. 2016-02-26. Fibred Fibration Categories. https://doi.org/10.1109/lics.2017.8005084

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