Surjectivity need not be preserved by group localizations

Gemma Bastardas

doi:10.1016/S0022-4049(01)00121-9

Surjectivity need not be preserved by group localizations

Gemma Bastardas

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	165-170
Journal	Journal of Pure and Applied Algebra
Volume	171
Issue number	2-3
DOIs	https://doi.org/10.1016/S0022-4049(01)00121-9
Publication status	Published - 25 Jun 2002

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AB - 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.

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