<abstract xmlns="http://www.w3.org/1999/xhtml">Given 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<italic>∇</italic>A splits, where <italic>∇</italic>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.</abstract>

Given 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.

Extensional quotient coalgebras

Department of Mathematics, Faculty of Science

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Extensional quotient coalgebras"}

Given 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...

Extensional quotient coalgebras

Publié en ligne: 07 mars 2018

Pages: 303 - 323

Reçu: 01 août 2015

DOI: https://doi.org/10.1515/ausm-2017-0023

Mots clés
bisimulation, congruence relation

© 2017 Jean-Paul Mavoungou, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Extensional quotient coalgebras

Publié en ligne: 07 mars 2018

Pages: 303 - 323

Reçu: 01 août 2015

DOI: https://doi.org/10.1515/ausm-2017-0023

Mots clésbisimulation, congruence relation

© 2017 Jean-Paul Mavoungou, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
bisimulation, congruence relation