Tape Diagrams for Monoidal Monads

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.