Transport of structure in higher homological algebra
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.
Keywords
Cite
@article{arxiv.2003.02254,
title = {Transport of structure in higher homological algebra},
author = {Raphael Bennett-Tennenhaus and Amit Shah},
journal= {arXiv preprint arXiv:2003.02254},
year = {2024}
}
Comments
v3: 24 pages; minor typographical changes; accepted in Journal of Algebra