Transport of structure in higher homological algebra

Bennett-Tennenhaus R, Shah A (2021)
Journal of Algebra 574: 514-549.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
Transport of structure; Higher homological algebra; Skeleton; n-exangulated category; (n+2)-angulated category; n-exact category; n-abelian category; n-exangulated functor; Extriangulated functor
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Algebra
Band
574
Seite(n)
514-549
ISSN
0021-8693
eISSN
1090-266X
Page URI
https://pub.uni-bielefeld.de/record/2953814

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Bennett-Tennenhaus R, Shah A. Transport of structure in higher homological algebra. Journal of Algebra. 2021;574:514-549.
Bennett-Tennenhaus, R., & Shah, A. (2021). Transport of structure in higher homological algebra. Journal of Algebra, 574, 514-549. https://doi.org/10.1016/j.jalgebra.2021.01.019
Bennett-Tennenhaus, R., and Shah, A. (2021). Transport of structure in higher homological algebra. Journal of Algebra 574, 514-549.
Bennett-Tennenhaus, R., & Shah, A., 2021. Transport of structure in higher homological algebra. Journal of Algebra, 574, p 514-549.
R. Bennett-Tennenhaus and A. Shah, “Transport of structure in higher homological algebra”, Journal of Algebra, vol. 574, 2021, pp. 514-549.
Bennett-Tennenhaus, R., Shah, A.: Transport of structure in higher homological algebra. Journal of Algebra. 574, 514-549 (2021).
Bennett-Tennenhaus, Raphael, and Shah, Amit. “Transport of structure in higher homological algebra”. Journal of Algebra 574 (2021): 514-549.

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