Document Type
Article
Publication Date
2023
Journal Title
Logical Methods in Computer Science
Volume Number
19
Issue Number
2
DOI
https://doi.org/10.46298/lmcs-19(2:1)2023
Version
Publisher PDF: the final published version of the article, with professional formatting and typesetting
Creative Commons License
This work is licensed under a CC BY License.
Disciplines
Mathematics
Abstract
We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as LNL polycategories, including LNL adjunctions, linear exponential comonads, LNL multicategories, IL-indexed categories, linearly distributive categories with storage, commutative and strong monads, CBPV-structures, models of polarized calculi, Freyd-categories, and skew multicategories, as well as ordinary cartesian, symmetric, and planar multicategories and monoidal categories, symmetric polycategories, and linearly distributive and *-autonomous categories. To study such classes of structures uniformly, we define a notion of LNL doctrine, such that each of these classes of structures can be identified with the algebras for some such doctrine. We show that free algebras for LNL doctrines can be presented by a sequent calculus, and that every morphism of doctrines induces an adjunction between their 2-categories of algebras.
Digital USD Citation
Shulman, Michael, "LNL Polycategories and Doctrines of Linear Logic" (2023). Mathematics: Faculty Scholarship. 8.
https://digital.sandiego.edu/mathematics-faculty/8