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# Small Congruences and Concreteness

Magdalena Velebilová
Proceedings of the American Mathematical Society
Vol. 115, No. 1 (May, 1992), pp. 13-18
DOI: 10.2307/2159558
Stable URL: http://www.jstor.org/stable/2159558
Page Count: 6
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## Abstract

Let $\underline K$ be a concrete category and ∼ a congruence on $\underline K$. Let ∼ be generated by a class M = M1 ∪ M2 of pairs of $\underline K$-morphisms such that $\{\operatorname{dom} f; (\exists g)((f, g) \in \mathscr{M}_1)\}$ and $\{\operatorname{rng} f; (\exists g)((f, g) \in \mathscr{M}_2)\}$ are small sets. Then $\underline K/\sim$ is concrete. Consequently, if ∼ is generated by a small set of pairs of morphisms, then $\underline K/\sim$ is concrete.

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