Monoidal bicategories, differential linear logic, and analytic functors
Category Theory
2025-09-17 v3 Logic in Computer Science
Logic
Abstract
We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation, introduced to study differential linear logic via differential categories. As an application, we extend the differential calculus of Joyal's analytic functors to analytic functors between presheaf categories, just as ordinary calculus extends from a single variable to many variables.
Cite
@article{arxiv.2405.05774,
title = {Monoidal bicategories, differential linear logic, and analytic functors},
author = {M. Fiore and N. Gambino and M. Hyland},
journal= {arXiv preprint arXiv:2405.05774},
year = {2025}
}
Comments
v3: made Theorem 3.11 more explicit (and adapted Remark 4.16 accordingly); rephrased Definition 3.13 and Hypothesis 7.1 in terms of canonical maps; fixed typos, added reference to [Fox76]. 49 pages. Comments welcome