City Research Online

Abstract

Suppose is an n-exangulated category. We show that the idempotent completion and the weak idempotent completion of are again n-exangulated categories. Furthermore, we also show that the canonical inclusion functor of into its (resp. weak) idempotent completion is n-exangulated and 2-universal among n-exangulated functors from to (resp. weakly) idempotent complete n-exangulated categories. Furthermore, we prove that if is n-exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and -angulated cases. However, our constructions recover the known structures in the established cases up to n-exangulated isomorphism of n-exangulated categories.

Publication Type:	Article
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher Keywords:	Additive category, Idempotent completion, Karoubi envelope, n-exangulated category, n-exangulated functor, n-exangulated natural transformation, Split idempotents, Weak idempotent completion
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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