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ISSN 1088-6826(e) ISSN 0002-9939(p)

Covers in finitely accessible categories

Author(s): Septimiu Crivei; Mike Prest; Blas Torrecillas
Journal: Proc. Amer. Math. Soc. 138 (2010), 1213-1221.
MSC (2010): Primary 18E05, 18C35; Secondary 16D90
Posted: December 1, 2009
MathSciNet review: 2578515
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Abstract | References | Similar articles | Additional information

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, ``Babes-Bolyai'' University, Str. Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania
Email: crivei@math.ubbcluj.ro

Mike Prest
Affiliation: School of Mathematics, Jan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email: mprest@manchester.ac.uk

Blas Torrecillas
Affiliation: Departamento de Álgebra y Análisis, Universidad de Almería, 04071 Almería, Spain
Email: btorreci@ual.es

DOI: 10.1090/S0002-9939-09-10178-8
PII: S 0002-9939(09)10178-8
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
Posted: 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
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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