City Research Online

Abstract

Integral categories form a sub-class of pre-abelian categories whose systematic study was initiated by Rump in 2001. In the first part of this article we determine whether several categories of topological and bornological vector spaces are integral. Moreover, we establish that the class of integral categories is not contained in the class of quasi-abelian categories, and that there exist semi-abelian categories that are neither integral nor quasi-abelian. In the last part of the article we show that a category is quasi-abelian if and only if it has admissible intersections, in the sense considered recently by Br¨ustle, Hassoun and Tattar. This exhibits that a rich class of non-abelian categories having this property arises naturally in functional analysis.

Publication Type:	Article
Additional Information:	This article has been published in its final form in Cahiers de topologie et géométrie différentielle catégoriques and it's available online at: https://cahierstgdc.com/wp-content/uploads/2021/07/Hassoun-Shah-Wegner-LXII-3.pdf
Publisher Keywords:	ntegral category, quasi-abelian category, projective object, quasi-projective object, topological vector space, bornological vector space, exact category, admissible intersections.
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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