Surjectivity need not be preserved by group localizations

Gemma Bastardas

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    Several examples studied in the literature motivate the question of whether or not all idempotent functors in the category of groups carry surjective homomorphisms into surjective homomorphisms. We negatively answer this question by giving a necessary and sufficient condition under which an idempotent functor on groups preserves surjectivity, and by displaying counterexamples which do not satisfy this condition. Our examples yield subcategories of groups, where epimorphisms need not be surjective. © 2002 Elsevier Science B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)165-170
    JournalJournal of Pure and Applied Algebra
    Volume171
    Issue number2-3
    DOIs
    Publication statusPublished - 25 Jun 2002

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