Layered Monoidal Theories II: Fibrational Semantics
Leo Lobski, Fabio Zanasi
TL;DR
This paper develops a categorical framework for layered monoidal theories, introducing models for fibrational, opfibrational, and deflational theories, and establishing their soundness and completeness.
Contribution
It introduces models for three classes of layered monoidal theories and connects them to established categorical structures like Grothendieck fibrations.
Findings
Models for fibrational, opfibrational, and deflational theories are sound and complete.
Connections established between layered monoidal theories and categorical structures.
Framework enhances understanding of theories at different abstraction levels.
Abstract
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Logic, programming, and type systems