Transport of structure in higher homological algebra

• Published in: Journal of algebra 2021-05, Vol.574, p.514-549
• Main Authors: Bennett-Tennenhaus, Raphael, Shah, Amit
• Format: Article
• Language: English
• Subjects: [formula omitted]-angulated category; Extriangulated functor; Higher homological algebra; n-abelian category; n-exact category; n-exangulated category; n-exangulated functor; Skeleton; Transport of structure
• ISSN: 0021-8693; 1090-266X
• DOI: 10.1016/j.jalgebra.2021.01.019

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.