English

Logical Aspects of Virtual Double Categories

Category Theory 2025-02-03 v2

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.

Keywords

Cite

@article{arxiv.2501.17869,
  title  = {Logical Aspects of Virtual Double Categories},
  author = {Hayato Nasu},
  journal= {arXiv preprint arXiv:2501.17869},
  year   = {2025}
}

Comments

103 pages, Master's thesis

R2 v1 2026-06-28T21:24:22.184Z