English

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.

Keywords

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

R2 v1 2026-07-01T10:52:54.639Z