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On Characterizing Injective Sheaves: Corrigendum

Published online by Cambridge University Press:  20 November 2018

David E. Dobbs
David E. Dobbs*
Affiliation:
University of Tennessee, Knoxville, Tennessee
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B. Banaschewski [1] has produced a counterexample to [2, Theorem 6]. As noted in [1, Remark 1], our error occurs in the final paragraph of the purported proof of [2, Theorem 6], for P need not be a subpresheaf of I. Accordingly, it remains an open problem to find an analogue of [2, Proposition 1] in the context of Boolean spaces. We hope that attacks on this problem will be facilitated by the (valid) initial three paragraphs of the argument given for [2, Theorem 6].

The following alterations to [2] are in order. Example 5, being a corollary of Theorem 6, remains doubtful, although the special case noted on pp. 1034-1035 is not affected. In Corollary 7, the assertion that j preserves infectives remains doubtful, although the proof for divisibility of j(M)(G) is valid.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 6 , 01 December 1980 , pp. 522
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Banaschewski, B., Injective sheaves of abelian groups: a counterexample, Can. J. Math., to appear.Google Scholar
2. Dobbs, David E., On characterizing injective sheaves, Can. J. Math. 29 (1977), 1031–1039.Google Scholar