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 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 sp...
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2017-12-01
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| Series: | Acta Universitatis Sapientiae: Mathematica |
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| Online Access: | https://doi.org/10.1515/ausm-2017-0023 |
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doaj-a6d1d052e2a049a6a5fdbb2a976a22592021-09-06T19:40:20ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522017-12-019230332310.1515/ausm-2017-0023ausm-2017-0023Extensional quotient coalgebrasMavoungou Jean-Paul0Department of Mathematics, Faculty of Science, University of Yaoundé 1, CameroonGiven 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.https://doi.org/10.1515/ausm-2017-0023bisimulationcongruence relation68q85 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mavoungou Jean-Paul |
| spellingShingle |
Mavoungou Jean-Paul Extensional quotient coalgebras Acta Universitatis Sapientiae: Mathematica bisimulation congruence relation 68q85 |
| author_facet |
Mavoungou Jean-Paul |
| author_sort |
Mavoungou Jean-Paul |
| title |
Extensional quotient coalgebras |
| title_short |
Extensional quotient coalgebras |
| title_full |
Extensional quotient coalgebras |
| title_fullStr |
Extensional quotient coalgebras |
| title_full_unstemmed |
Extensional quotient coalgebras |
| title_sort |
extensional quotient coalgebras |
| publisher |
Sciendo |
| series |
Acta Universitatis Sapientiae: Mathematica |
| issn |
2066-7752 |
| publishDate |
2017-12-01 |
| description |
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. |
| topic |
bisimulation congruence relation 68q85 |
| url |
https://doi.org/10.1515/ausm-2017-0023 |
| work_keys_str_mv |
AT mavoungoujeanpaul extensionalquotientcoalgebras |
| _version_ |
1717768707051094016 |