Abstract.
In a category with injective hulls and a cogenerator, the embeddings into injective hulls can never form a natural transformation, unless all objects are injective. In particular, assigning to a field its algebraic closure, to a poset or Boolean algebra its Mac-Neille completion, and to an R-module its injective envelope is not functorial, if one wants the respective embeddings to form a natural transformation.
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Received January 21, 2000; accepted in final form August 10, 2001.
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ID="h1"The hospitality of York University is gratefully acknowledged by the first author.
ID="h2"Third author partially supported by the Grant Agency of the Czech Republic under Grant no. 201/99/0310, and the hospitality of York University is also acknowledged.
ID="h3"Partial financial assistance by the Natural Sciences and Engineering Councel of Canada is acknowledged by the fourth author.
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Adámek, J., Herrlich, H., Rosický, J. et al. Injective hulls are not natural. Algebra univers. 48, 379–388 (2002). https://doi.org/10.1007/s000120200006
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DOI: https://doi.org/10.1007/s000120200006