Tape Diagrams for Monoidal Monads
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912300245450752 |
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| author | Bonchi, Filippo Cioffo, Cipriano Junior Di Giorgio, Alessandro Di Lavore, Elena |
| author_facet | Bonchi, Filippo Cioffo, Cipriano Junior Di Giorgio, Alessandro Di Lavore, Elena |
| contents | Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, $\oplus$ and $\otimes$, where $\otimes$ distributes over $\oplus$. However, their applicability is limited to categories where $\oplus$ is a biproduct, i.e., both a categorical product and a coproduct. In this work, we extend tape diagrams to deal with Kleisli categories of symmetric monoidal monads, presented by algebraic theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tape Diagrams for Monoidal Monads Bonchi, Filippo Cioffo, Cipriano Junior Di Giorgio, Alessandro Di Lavore, Elena Logic in Computer Science Category Theory Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, $\oplus$ and $\otimes$, where $\otimes$ distributes over $\oplus$. However, their applicability is limited to categories where $\oplus$ is a biproduct, i.e., both a categorical product and a coproduct. In this work, we extend tape diagrams to deal with Kleisli categories of symmetric monoidal monads, presented by algebraic theories. |
| title | Tape Diagrams for Monoidal Monads |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2503.22819 |