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The Existence of Injective Effacements

Published online by Cambridge University Press:  20 November 2018

Michael Barr
Michael Barr*
Affiliation:
Department of Mathematics, McGill UniversityP.O. Box 6070 Montreal 101, Canada
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The main result of this paper is little more than a juxtaposition of a remark in [Leroux] (§5, part A), with a theorem of [Banaschewski]. However, the results are individually little known and their juxtaposition not at all. More explicitly, Leroux remarks, in somewhat different form,

Let the category X be complete and cocomplete, and have a set of cogenerators. Then a necessary and sufficient condition that there exist infective effacements (with respect to the class of regular monomorphisms) is that X be coregular and satisfy, in addition, condition COEX 4*.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 1 - 6
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Banaschewski, B., Projective covers in categories of topological spaces and topological algebras, "Proceedings of the Topology Conference", Kanpur, 1968, (to appear).Google Scholar
2. Barr, M., Exact categories, in "Exact Categories and Categories of Sheaves", Lecture Notes in Mathematics 236 (1971), 1-120.Google Scholar
3. Leroux, P., Sur les structures d'effacement, Math. Z. 121 (1971), 329-340.Google Scholar