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Doctrines, modalities and comonads

Published online by Cambridge University Press:  14 September 2021

Francesco Dagnino  and
Giuseppe Rosolini Open the ORCID record for Giuseppe Rosolini [Opens in a new window]
Francesco Dagnino
Affiliation:
DIBRIS, Università di Genova
Giuseppe Rosolini*
Affiliation:
DIMA, Università di Genova
*
*Corresponding author. Email: rosolini@unige.it
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Abstract

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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 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.

Keywords

Modal operatordoctrineadjunctioncomonadtemporal logicslinear logic
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Special Issue 7: The Power Festschrift , August 2021 , pp. 769 - 798
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re- use, distribution and reproduction, provided the or article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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