Tape Diagrams for Monoidal Monads

2025/03/28 by Bonchi, Filippo, Cioffo, Cipriano Junior, Di Giorgio, Alessandro +1 · 1 citation
#Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2503.22819

Abstract

Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, ⊕ and ⊗, where ⊗ distributes over ⊕. However, their applicability is limited to categories where ⊕ 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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