## 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.

Originalsprog Engelsk Journal of Algebra 574 514-549 36 0021-8693 https://doi.org/10.1016/j.jalgebra.2021.01.019 Udgivet - 15 maj 2021 Ja

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