Yet another cubical type theory, but via a semantic approach

Chris Kapulkin; Yufeng Li

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arXiv · 2512.17548

Yet another cubical type theory, but via a semantic approach

Chris Kapulkin·Yufeng Li

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Abstract

We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to Uemura's categories with representable morphisms. In particular, we show that this new type theory admits an interpretation in a wide variety of settings, including simplicial sets and cartesian cubical sets.

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Chris Kapulkin, Yufeng Li. 2025-12-19. Yet another cubical type theory, but via a semantic approach. https://arxiv.org/abs/2512.17548

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