On Doctrines and Cartesian Bicategories
Logic in Computer Science
2021-11-09 v1 Category Theory
Abstract
We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in algebraic terms based on a string diagrammatic calculus, the latter in universal terms using the fundamental notion of adjoint functor. We prove that these two approaches are related by an adjunction, which can be strengthened to an equivalence by imposing further constraints on doctrines.
Cite
@article{arxiv.2106.08142,
title = {On Doctrines and Cartesian Bicategories},
author = {Filippo Bonchi and Alessio Santamaria and Jens Seeber and Paweł Sobociński},
journal= {arXiv preprint arXiv:2106.08142},
year = {2021}
}