# 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

, Volume 9 (2): 21 – Dec 1, 2017
21 pages

/lp/degruyter/extensional-quotient-coalgebras-SQtxDHGy4y
Publisher
de Gruyter
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

Published: Dec 1, 2017

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