Injective hulls are not natural

Springer Science and Business Media LLC - Tập 48 - Trang 379-388 - 2002
Jiří Adámek1, Horst Herrlich2, Jiří Rosický3, Walter Tholen4
1Intitut für Theoretische Informatik, Technische Universität Braunschweig, 38032 Braunschweig, Germany, e-mail: [email protected], , DE
2Fachbereich Mathematik, Universität Bremen, 28334 Bremen, Germany, e-mail: [email protected], , DE
3Department of Mathematics, Masaryk University, 66295 Brno, Czech Republic, e-mail: [email protected], , CZ
4Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada, e-mail: [email protected], , CA

Tóm tắt

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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Springer Science and Business Media LLC

Tập 48

379-388

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