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.
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References
Adámek. J.,Theory of Mathematical Structures. D. Reidel Publishing Company, Dordrecht, 1983.
Rosenberg, I. G. andSturm, T.,Congruence relations on finitary models. Czech. Math. J. (1992), in print.
Sturm, T.,Verbände von Kernen isotoner Abbildungen. Czech. Math. J.22 (1972), 126–144.
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I am indebted to Professor Teo Sturm as this paper originated from his seminar series on Algebraic Structures.
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Jordens, O. Two equivalent definitions of a congruence on a finitary model in a quasivariety. Algebra Universalis 29, 513–520 (1992). https://doi.org/10.1007/BF01190778
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DOI: https://doi.org/10.1007/BF01190778