Beck–Chevalley condition and Goursat categories
We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted Beck–Chevalley condition, with respect to the fibration of po...
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| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2017
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| Texto completo: | http://hdl.handle.net/10316/89464 |
| País: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/89464 |
| Resumo: | We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted Beck–Chevalley condition, with respect to the fibration of points, for a special class of commutative squares. In the case of varieties of universal algebras these results give, in particular, a structural explanation of the existence of the ternary operations characterising 3-permutable varieties of universal algebras. |
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