# Tape Diagrams for Monoidal Monads

arXiv: https://arxiv.org/abs/2503.22819 · HTML: https://mlsanity.com/paper/2503.22819/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2025.

## Built on by (most cited first, 1 of 1)

- [Graphical einops: bridging tensor networks and computation graphs](https://mlsanity.com/paper/2605.31485/) (2026)

## Abstract (arXiv)

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.