Two equivalent definitions of a congruence on a finitary model in a quasivariety |
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Authors: | Olav Jordens |
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Affiliation: | (1) Department of Mathematics, University of Natal, King George V Avenue, 4001 Durban, South Africa |
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Abstract: | LetL be a finitary language and letK be a subcategory of the category of allL-models andL-morphisms. For aK-objectA we consider two definitions of aK-congruence relation onA: that given by Rosenberg and Sturm [2], and that given by Adámek [1]. Both definitions are external definitions in the sense that they depend on the otherK-objects. IfK is a full subcategory, such that theK-objects form a quasivariety, then it is shown that the definitions ofK-congruence are equivalent and a purely internal characterisation is given.Presented by I. Rosenberg.I am indebted to Professor Teo Sturm as this paper originated from his seminar series on Algebraic Structures. |
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