PUB - Publikationen an der Universität Bielefeld

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. (C) 2021 Elsevier Inc. All rights reserved.