String Diagrams for Closed Symmetric Monoidal Categories
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915659237031936 |
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| author | Reader, Callum Di Giorgio, Alessandro |
| author_facet | Reader, Callum Di Giorgio, Alessandro |
| contents | We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules.
We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | String Diagrams for Closed Symmetric Monoidal Categories Reader, Callum Di Giorgio, Alessandro Logic in Computer Science Category Theory We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics. |
| title | String Diagrams for Closed Symmetric Monoidal Categories |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2512.06499 |