Geodesic
Representations of concrete categories in the category of sets
Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 125-127.

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An example of a concrete category which cannot be isomorphically embedded in the category of sets such that all monomorphisms are represented by injections is specified. 
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     author = {M. S. Tsalenko},
     title = {Representations of concrete categories in the category of sets},
     journal = {Matemati\v{c}eskie zametki},
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     number = {1},
     year = {1969},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a15/}
}
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M. S. Tsalenko. Representations of concrete categories in the category of sets. Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 125-127. http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a15/