Promonads and String Diagrams for Effectful Categories

05/16/2022

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by   Mario Román, et al.

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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.