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categories: Preprint: a paper on injective hulls
This is to announce a paper that can be obtained as "Paper3-2000.ps"
on the address ftp://ftp.iti.cs.tu-bs.de/pub/staff/adamek
TITLE: Injective Hulls are not Natural
AUTHORS: J. Adamek, H. Herrlich, J. Rosicky and W. Tholen
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 MacNeille
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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