nLab LNL polycategory


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:


Introduced in

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