On the Centre of Strong Graded Monads
Flavien Breuvart, Quan Long, Vladimir Zamdzhiev
TL;DR
This paper introduces the concept of 'centre' for pomonoid-graded strong monads, generalizing previous work, and shows how it leads to a graded commutative submonad, connecting to duoidally-graded strong monads.
Contribution
It defines the 'centre' for pomonoid-graded strong monads and explores its implications for graded commutativity and relations to duoidally-graded monads.
Findings
The 'centre' determines a pomonoid-graded commutative submonad.
Existence of the centre influences the structure of the monad.
Connections between graded strong monads and duoidally-graded monads are established.
Abstract
We introduce the notion of 'centre' for pomonoid-graded strong monads which generalizes some previous work that describes the centre of (not graded) strong monads. We show that, whenever the centre exists, this determines a pomonoid-graded commutative submonad of the original one. We also discuss how this relates to duoidally-graded strong monads.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Fuzzy and Soft Set Theory