A *linear-non-linear polycategory* or simply *LNL polycategory* is a generalization of a symmetric polycategory to include “non-linear” objects in the same way that linear-non-linear logic generalizes symmetric multicategories. Just as linear-non-linear logic provides a setting in which the exponential comonad ! in intuitionistic linear logic can be decomposed into an adjunction, LNL polycategories provide a setting in which the exponential comonad ! and the monad ? in classical linear logic can each be decomposed into adjunctions.

In addition to the study of classical linear-logic, LNL polycategories can be used as a unified setting in which to study multicategory and polycategory-like structures as “LNL doctrines”.

See the original paper for a definition of LNL doctrine.

The following is an incomplete list of structures that can be defined as LNL doctrines:

- cartesian multicategories
- symmetric multicategories
- symmetric polycategories?
- linear-non-linear logic
- skew-multicategories?
- call-by-push-value
- Freyd multicategories
- adjunctions
- models of classical linear logic

Introduced in

- Michael Shulman,
*LNL polycategories and doctrines of linear logic*, arxiv

Last revised on August 24, 2022 at 15:55:04. See the history of this page for a list of all contributions to it.