Monoidal bicategories, differential linear logic, and analytic functors

TL;DR

This paper advances the theory of monoidal bicategories by integrating concepts from linear logic and differential calculus, extending analytic functors to a multivariable setting within presheaf categories.

Contribution

It introduces bicategorical versions of linear exponential comonads and coderelictions, connecting monoidal bicategories with differential linear logic and analytic functors.

Findings

Developed bicategorical counterparts of linear exponential comonads and coderelictions.

Extended differential calculus of analytic functors to multivariable cases.

Bridged monoidal bicategories with differential linear logic and analytic functor theory.

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.