Small congruences and concreteness

Velebilová, Magdalena

doi:10.1090/S0002-9939-1992-1079899-X

Small congruences and concreteness
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by Magdalena Velebilová

Proc. Amer. Math. Soc. 115 (1992), 13-18

DOI: https://doi.org/10.1090/S0002-9939-1992-1079899-X

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Abstract:

Let $\underline K$ be a concrete category and $\sim$ a congruence on $\underline K$ . Let $\sim$ be generated by a class $M = {M_1} \cup {M_2}$ of Pairs of $\underline K$-morphisms such that $\{ \operatorname {dom} f;(\exists g)((f,g) \in {M_1})\}$ and $\left \{ {\operatorname {rng} f;(\exists g)((f,g) \in {M_2})} \right \}$ are small sets. Then $\underline K / \sim$ is concrete. Consequently, if $\sim$ is generated by a small set of pairs of morphisms, then $\underline K / \sim$ is concrete.

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