Bennett-Tennenhaus, R and Shah, A orcid.org/0000-0002-6623-8228 (2021) Transport of structure in higher homological algebra. Journal of Algebra, 574. pp. 514-549. ISSN 0021-8693
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. |
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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Mar 2021 15:29 |
Last Modified: | 01 Feb 2022 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jalgebra.2021.01.019 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:172297 |