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arXiv · 2501.17869

Logical Aspects of Virtual Double Categories

Hayato Nasu
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Abstract

This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is bringing together the semantics and the syntax of logical systems in a common categorical framework. This thesis is intended to propose a double-categorical method for categorical logic in line with this principle. On the semantic side, we investigate virtual double categories as a model of predicate logic and illustrate that this framework subsumes the existing frameworks properly. On the syntactic side, we develop a type theory called FVDblTT that is designed as an internal language for virtual double categories.

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Hayato Nasu. 2025-01-15. Logical Aspects of Virtual Double Categories. https://arxiv.org/abs/2501.17869

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