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：Premonoidal 和 Freyd 类别均按非cartesian Freyd 类别( 有效类别) 普遍分类。 我们为带有自由添加对象的一分子类的字符串图中有效类别构建字符串图。 我们显示, 有效类别是具有合适高压产品的单分子双类线类中的伪分子。