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A COCOMPLETE BUT NOT COMPLETE ABELIAN CATEGORY

Part of: Abelian categories

Published online by Cambridge University Press:  05 February 2020

JEREMY RICKARD Open the ORCID record for JEREMY RICKARD [Opens in a new window]
JEREMY RICKARD*
Affiliation:
School of Mathematics, University of Bristol, BristolBS8 1TW, UK email [email protected]
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Abstract

An example of a cocomplete abelian category that is not complete is constructed.

Keywords

abelian categoriescocompleteness

MSC classification

Primary: 18E10: Exact categories, abelian categories
Secondary: 18E15: Grothendieck categories
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 442 - 445
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

Adámek, J. and Rosický, J., Locally Presentable and Accessible Categories, London Mathematical Society Lecture Note Series, 189 (Cambridge University Press, Cambridge, 1994).CrossRefGoogle Scholar
Grothendieck, A., ‘Sur quelques points d’algèbre homologique’, Tohoku Math. J. (2) 9 (1957), 119–221.Google Scholar
Kashiwara, M. and Schapira, P., Categories and Sheaves, Grundlehren der mathematischen Wissenschaften, 332 (Springer, Berlin, 2006).10.1007/3-540-27950-4CrossRefGoogle Scholar
Virili, S., ‘Cocomplete but not complete abelian category’, MathOverflow (2012), https://mathoverflow.net/q/112574.Google Scholar