We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in algebraic terms based on a string diagrammatic calculus, the latter in universal terms using the fundamental notion of adjoint functor. We prove that these two approaches are related by an adjunction, which can be strengthened to an equivalence by imposing further constraints on doctrines.

翻译：这两种理论都提供了不同的方法来抽象逻辑系统的结构特性:前者基于一个字符串图表计算法的代数术语,后者以通用的术语使用联合伴奏者的基本概念。 我们证明这两种方法都与一种辅助方法有关,可以通过对理论施加进一步的限制而加强这种等同。