Extensional quotient coalgebras

Extensional quotient coalgebras AbstractGiven an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence relations on an F-coalgebra (A, a) is called a coatomic congruence relation on (A, a). Besides, a coatomic congruence relation K is said to be factor split if the canonical homomor-phism ν : AK → A∇A splits, where ∇A is the largest congruence relation on (A, a). Assuming that F is a covarietor which preserves regular monos, we prove under suitable assumptions on the underlying category that, every quotient coalgebra can be made extensional by taking the regular quotient of an F-coalgebra with respect to a coatomic and not factor split congruence relation or its largest congruence relation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Universitatis Sapientiae, Mathematica de Gruyter

Extensional quotient coalgebras

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Publisher
De Gruyter Open
Copyright
© 2017 Jean-Paul Mavoungou, published by De Gruyter Open
eISSN
2066-7752
D.O.I.
10.1515/ausm-2017-0023
Publisher site
See Article on Publisher Site

Abstract

AbstractGiven an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence relations on an F-coalgebra (A, a) is called a coatomic congruence relation on (A, a). Besides, a coatomic congruence relation K is said to be factor split if the canonical homomor-phism ν : AK → A∇A splits, where ∇A is the largest congruence relation on (A, a). Assuming that F is a covarietor which preserves regular monos, we prove under suitable assumptions on the underlying category that, every quotient coalgebra can be made extensional by taking the regular quotient of an F-coalgebra with respect to a coatomic and not factor split congruence relation or its largest congruence relation.

Journal

Acta Universitatis Sapientiae, Mathematicade Gruyter

Published: Dec 1, 2017

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