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On the radical of a category

Published online by Cambridge University Press:  09 April 2009

G. M. Kelly
G. M. Kelly
Affiliation:
The University of Sydney.
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In [1] the concept of completeness of a functor was introduced and, in the cse of additive * categories and and an additive functor T: → , a criterion for T (supposed surjective) to be complete was given in terms of the kernel of T: this was that for each object A of the ideal A should be containded in the (Jacobson) radical of A. (The meaning of this notation and nomemclature is recalled in § 2 below). The question arises whether in any additive category there is a greatest ideal with this property, so that the canonical functor T: → / is in some sense the coarsest that faithfully represents the objects (but not the maps) of .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 3 , August 1964 , pp. 299 - 307
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Kelly, G. M., Complete functors in homology. I., Proc. camb. Phil. Soc. (to appear).Google Scholar