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arXiv · 1904.04097

A General Framework for the Semantics of Type Theory

Taichi Uemura
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Abstract

We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory: every type theory has a bi-initial model; every model of a type theory has its internal language; the category of theories over a type theory is bi-equivalent to a full sub-2-category of the 2-category of models of the type theory.

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Taichi Uemura. 2019-04-08. A General Framework for the Semantics of Type Theory. https://doi.org/10.1017/s0960129523000208

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