On Characterizing Injective Sheaves: Corrigendum
Canadian journal of mathematics, Tome 32 (1980) no. 6, p. 522
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Dobbs, David E. On Characterizing Injective Sheaves: Corrigendum. Canadian journal of mathematics, Tome 32 (1980) no. 6, p. 522. doi: 10.4153/CJM-1980-120-5
@article{10_4153_CJM_1980_120_5,
author = {Dobbs, David E.},
title = {On {Characterizing} {Injective} {Sheaves:} {Corrigendum}},
journal = {Canadian journal of mathematics},
pages = {522--522},
year = {1980},
volume = {32},
number = {6},
doi = {10.4153/CJM-1980-120-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-120-5/}
}
[1] 1. Banaschewski, B., Injective sheaves of abelian groups: a counterexample, Can. J. Math., to appear. Google Scholar
[2] 2. Dobbs, David E., On characterizing injective sheaves, Can. J. Math. 29 (1977), 1031–1039. Google Scholar
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