LNL polycategories

Michael Shulman

University of San Diego




Abstract: A multicategory is a categorical structure of "multi-morphisms", whose domains are finite lists of objects rather than single ones. This enables the characterization of tensor products by a universal property, as well as a closer match to the syntax of intuitionistic multiplicative linear logic. Similarly, Szabo's "polycategories" allow both domains and codomains to be lists of objects, enabling a universal characterization of linearly-distributive and star-autonomous structure, and a closer match to the syntax of classical multiplicative linear logic.

In this talk I will introduce "LNL polycategories", which extend these correspondences to full linear logic with exponentials, corresponding to LNL adjunctions on monoidal categories. LNL polycategories are a very rich structure that specialize to a wide variety of notions in the literature; I will also sketch how these specializations can be treated uniformly with a fibrational notion of "doctrine".