Injective hulls are not natural
by
Jiri Adamek
Technical University of Braunschweig
Coauthors: Horst Herrlich, Jiri Rosicky, Walter Tholen

The formation of injective hulls in a category K (in which every object has an injective hull) is seldom natural in the sense of defining an endofunctor F of K together with a natutral transformation Id -> F. Thus neither MacNeille completion of posets, nor injective hull of modules are natural. There is, nevertheless, a general procedure of assigning naturally injective extensions to objects by using an iterative construction of "approximations" of injectivity. This construcion works well in locally presentable categories, as well as in the category of topological spaces. We introduce a class of categories, called locally ranked, in which this construction can be performed, and which include the above examples.

Date received: May 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-07.