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arXiv · 2212.02444

Homotopy type theory as a language for diagrams of $\infty$-logoses

Taichi Uemura
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Abstract

We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos but also a diagram of $\infty$-logoses. This also provides a higher dimensional version of Sterling's synthetic Tait computability -- a type theory for higher dimensional logical relations.

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Taichi Uemura. 2022-12-05. Homotopy type theory as a language for diagrams of $\infty$-logoses. https://doi.org/10.46298/lmcs-22(1%3A25)2026

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