2000 character limit reached
Promonads and String Diagrams for Effectful Categories (2205.07664v4)
Published 16 May 2022 in math.CT and cs.LO
Abstract: Premonoidal and Freyd categories are both generalized by non-cartesian Freyd categories: effectful categories. We construct string diagrams for effectful categories in terms of the string diagrams for a monoidal category with a freely added object. We show that effectful categories are pseudomonoids in a monoidal bicategory of promonads with a suitable tensor product.