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Doctrines, modalities and comonads

Published online by Cambridge University Press:  14 September 2021

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.

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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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