Layered Monoidal Theories II: Fibrational Semantics
Category Theory
2026-02-27 v1 Logic in Computer Science
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.
Cite
@article{arxiv.2602.22373,
title = {Layered Monoidal Theories II: Fibrational Semantics},
author = {Leo Lobski and Fabio Zanasi},
journal= {arXiv preprint arXiv:2602.22373},
year = {2026}
}
Comments
50 pages, 9 figures