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：前单子范畴与弗雷德范畴均为非笛卡尔弗雷德范畴（即效应范畴）的推广。我们通过为具有自由添加对象的幺半范畴构造弦图，建立了效应范畴的弦图表示。研究表明，效应范畴可视为在带有适当张量积的普罗单子构成的幺半双范畴中的伪幺半群。