LNL polycategories
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".