Core Concepts
The author introduces a new model of linear logic using stabilized profunctors and stable species of structures, refining the bicategory of groupoids with Boolean kits to constrain profunctors.
Abstract
The content discusses the definition and application of stabilized profunctors and stable species of structures in a new bicategorical model of linear logic. It explores the connection between polynomial functors and analytic functors, emphasizing the role of kits in constraining profunctors. The paper establishes that the bicategory of groupoids with Boolean kits, stable species, and natural transformations is cartesian closed. Additionally, it delves into the logical structure underlying stabilized profunctors and their connection to classical linear logic.
Stats
An object in the new model is a groupoid with additional structure called a Boolean kit.
Stable species correspond to stable functors between full subcategories determined by kits.
The bicategory SProf has properties making it a model of linear logic.
Kits enforce free actions corresponding to finitary polynomial functors between categories.
The bicategory Prof has well-known logical features modeling linear logic.
Every analytic functor corresponds to a unique generating species up to isomorphism.
Finitary polynomial functors are identified as free analytic functors in special cases.
Kits on groupoids specify permitted stabilizers for structures' actions.
Boolean kits are defined as those closed under double orthogonality for models of classical systems.