City Research Online

Abstract

We fill a gap in the literature regarding ‘transport of structure’ for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing in (classical and higher) homological algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n+2)-angulated category is in fact what we call a strong (n+2)-angulated category. When n=1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n-exangulated functor between n-exangulated categories. This recovers the definition of an (n+2)-angulated functor when the categories concerned are (n+2)-angulated, and the higher analogue of an exact functor when the categories concerned are n-exact.

Publication Type:	Article
Additional Information:	© 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Transport of structure, Higher homological algebra, Skeleton, n-exangulated category, (n+2)-angulated category, n-exact category, n-abelian category, n-exangulated functor, Extriangulated functor
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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