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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Covers in finitely accessible categories

Authors: Septimiu Crivei, Mike Prest and Blas Torrecillas
Journal: Proc. Amer. Math. Soc. 138 (2010), 1213-1221
MSC (2010): Primary 18E05, 18C35; Secondary 16D90
Published electronically: December 1, 2009
MathSciNet review: 2578515
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Abstract: We show that in a finitely accessible additive category every class of objects closed under direct limits and pure epimorphic images is covering. In particular, the classes of flat objects in a locally finitely presented additive category and of absolutely pure objects in a locally coherent category are covering.

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Additional Information

Septimiu Crivei
Affiliation: Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania

Mike Prest
Affiliation: School of Mathematics, Jan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

Blas Torrecillas
Affiliation: Departamento de Álgebra y Análisis, Universidad de Almería, 04071 Almería, Spain

Keywords: Finitely accessible additive category, locally finitely presented additive category, (pre)cover, (pre)envelope, flat object, absolutely pure object
Received by editor(s): April 17, 2009
Received by editor(s) in revised form: August 1, 2009
Published electronically: December 1, 2009
Additional Notes: This work was partially supported by MEC Romania (grant PN-II-ID-PCE-2008-2 project ID_2271), MEC Spain and DGI Spain (project MTM2008-03339), and Junta de Andalucía (Proyecto de Excelencia FQM 3128). The first author would like to thank the Department of Algebra and Analysis for their kind hospitality during his stays at the University of Almería.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.