Doctrines, modalities and comonads
Category Theory
2023-06-22 v1 Logic in Computer Science
Logic
Abstract
Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-category Dtn of doctrines. Modal interior operators are characterised as particular adjoints in the 2-category Dtn. We show that they can be constructed from comonads in Dtn as well as from adjunctions in it, and the two constructions compare. Finally we show the amount of information lost in the passage from a comonad, or from an adjunction, to the modal interior operator. The basis for the present work is provided by some seminal work of John Power.
Keywords
Cite
@article{arxiv.2107.14031,
title = {Doctrines, modalities and comonads},
author = {Francesco Dagnino and Giuseppe Rosolini},
journal= {arXiv preprint arXiv:2107.14031},
year = {2023}
}