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arXiv · 2503.22819

Tape Diagrams for Monoidal Monads

Filippo Bonchi·Cipriano Junior Cioffo·Alessandro Di Giorgio·Elena Di Lavore
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Abstract

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.

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Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio, Elena Di Lavore. 2025-03-28. Tape Diagrams for Monoidal Monads. https://arxiv.org/abs/2503.22819

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