Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal theories: fibrational, opfibrational and deflational theories. We prove soundness and completeness of these theories for the respective models. Our work reveals connections between layered monoidal theories and well-known categorical structures such as Grothendieck fibrations and displayed categories.

翻译：分层幺半理论通过弦图代数，为在不同抽象层次上研究科学理论提供了一个范畴论框架。我们为三类密切相关的分层幺半理论——纤维化理论、反纤维化理论和紧缩化理论——引入了模型。我们证明了这些理论相对于各自模型的可靠性与完备性。我们的工作揭示了分层幺半理论与格罗滕迪克纤维化、展示范畴等著名范畴结构之间的联系。