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.

翻译：预幺半范畴与Freyd范畴均被非笛卡尔Freyd范畴（即效应范畴）所推广。我们通过添加自由对象的幺半范畴的弦图，为效应范畴构造了弦图表示。我们证明效应范畴是具有合适张量积的预幺半子幺半双范畴中的伪幺半群。