Injective hulls are not natural

被引：14

作者：

Adámek, J ^{[1
]}

Herrlich, H

Rosicky, J

Tholen, W

机构：

[1] Tech Univ Braunschweig, Inst Theoret Informat, D-38032 Braunschweig, Germany

[2] Univ Bremen, Fachbereich Math, D-28334 Bremen, Germany

[3] Masaryk Univ, Dept Math, Brno 66295, Czech Republic

[4] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

ALGEBRA UNIVERSALIS | 2002年 / 48卷 / 04期

关键词：

injective object; projective object; injective hull; projective cover;

D O I：

10.1007/s000120200006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：379 / 388

页数：10

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