Logical Aspects of Virtual Double Categories
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909470748049408 |
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| author | Nasu, Hayato |
| author_facet | Nasu, Hayato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logical Aspects of Virtual Double Categories Nasu, Hayato Category Theory 18N10, 03G30, 18C50, 18D70 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. |
| title | Logical Aspects of Virtual Double Categories |
| topic | Category Theory 18N10, 03G30, 18C50, 18D70 |
| url | https://arxiv.org/abs/2501.17869 |