Monoidal bicategories, differential linear logic, and analytic functors
arXiv:2405.05774
The paper defines bicategorical analogues of linear exponential comonads and codereliction transformations, connecting monoidal bicategories with differential linear logic, and uses these tools to extend Joyal’s analytic functor calculus to presheaf categories.
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.
v4: typos corrected; updated references. Accepted for publication in Journal of the European Mathematical Society