Doctrines, modalities and comonads
Francesco Dagnino, Giuseppe Rosolini · Mathematical Structures in Computer Science · 2021
Abstract Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-categoryDtnof doctrines. Modal interior operators are characterised as particular adjoints in the 2-categoryDtn. We show that they can be constructed from comonads inDtnas well as from adjunctions in it, and we compare the two constructions. 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.