TY - JOUR

T1 - Transport of structure in higher homological algebra

AU - Bennett-Tennenhaus, Raphael

AU - Shah, Amit

N1 - 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:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/5/15

Y1 - 2021/5/15

N2 - 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.

AB - 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.

KW - (n+2)-angulated category

KW - Extriangulated functor

KW - Higher homological algebra

KW - n-abelian category

KW - n-exact category

KW - n-exangulated category

KW - n-exangulated functor

KW - Skeleton

KW - Transport of structure

UR - http://www.scopus.com/inward/record.url?scp=85100456617&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.01.019

DO - 10.1016/j.jalgebra.2021.01.019

M3 - Journal article

AN - SCOPUS:85100456617

SN - 0021-8693

VL - 574

SP - 514

EP - 549

JO - Journal of Algebra

JF - Journal of Algebra

ER -