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Small congruences and concreteness


Author: Magdalena Velebilová
Journal: Proc. Amer. Math. Soc. 115 (1992), 13-18
MSC: Primary 18A32; Secondary 18B05
DOI: https://doi.org/10.1090/S0002-9939-1992-1079899-X
MathSciNet review: 1079899
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1079899-X
Keywords: Concrete category, congruence
Article copyright: © Copyright 1992 American Mathematical Society

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