Geodesic
Homomorphic images of subdirectly irreducible groupoids
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 443-450.

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A groupoid $H$ is a homomorphic image of a subdirectly irreducible groupoid $G$ (over its monolith) if and only if $H$ has a smallest ideal.
Classification : 08A30, 20N02
Keywords: groupoid; subdirect irreducibility 
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Stanovský, David. Homomorphic images of subdirectly irreducible groupoids. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 443-450. http://geodesic.mathdoc.fr/item/CMUC_2001__42_3_a1/