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Transport of structure in higher homological algebra

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  • Raphael Bennett-Tennenhaus, Bielefeld University
  • ,
  • Amit Shah

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.

Original languageEnglish
JournalJournal of Algebra
Pages (from-to)514-549
Number of pages36
Publication statusPublished - 15 May 2021
Externally publishedYes

Bibliographical note

Funding Information:
During part of this work the first author was supported by the Alexander von Humboldt Foundation in the framework of an Alexander von Humboldt Professorship endowed by the German Federal Ministry of Education and Research, for which they are grateful. The second author gratefully acknowledges support from the EPSRC (grant EP/P016014/1 ), and from the London Mathematical Society for funding through an Early Career Fellowship with support from Heilbronn Institute for Mathematical Research (grant ECF-1920-57 ). Some of this work was carried out as part of the second author's Ph.D. at the University of Leeds.

Publisher Copyright:
© 2021 Elsevier Inc.

Copyright 2021 Elsevier B.V., All rights reserved.

    Research areas

  • (n+2)-angulated category, Extriangulated functor, Higher homological algebra, n-abelian category, n-exact category, n-exangulated category, n-exangulated functor, Skeleton, Transport of structure

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