n-abelian and n-exact categories
(2016) In Mathematische Zeitschrift 283(3-4). p.703-759- Abstract
- We introduce n-abelian and n-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that n-cluster-tilting subcategories of abelian (resp. exact) categories are n-abelian (resp. n-exact). These results allow to construct several examples of n-abelian and n-exact categories. Conversely, we prove that n-abelian categories satisfying certain mild assumptions can be realized as n-cluster-tilting subcategories of abelian categories. In analogy with a classical result of Happel, we show that the stable category of a Frobenius n-exact category has a natural (n+2)-angulated structure in the sense of Geiß–Keller–Oppermann. We give several examples of n-abelian and n-exact... (More)
- We introduce n-abelian and n-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that n-cluster-tilting subcategories of abelian (resp. exact) categories are n-abelian (resp. n-exact). These results allow to construct several examples of n-abelian and n-exact categories. Conversely, we prove that n-abelian categories satisfying certain mild assumptions can be realized as n-cluster-tilting subcategories of abelian categories. In analogy with a classical result of Happel, we show that the stable category of a Frobenius n-exact category has a natural (n+2)-angulated structure in the sense of Geiß–Keller–Oppermann. We give several examples of n-abelian and n-exact categories which have appeared in representation theory, commutative algebra, commutative and non-commutative algebraic geometry. (Less)
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https://lup.lub.lu.se/record/fcfc94d3-cadc-48f4-8745-8cd849f346fe
- author
- Jasso, Gustavo LU
- publishing date
- 2016-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematische Zeitschrift
- volume
- 283
- issue
- 3-4
- pages
- 57 pages
- publisher
- Springer
- external identifiers
-
- scopus:84954549373
- ISSN
- 0025-5874
- DOI
- 10.1007/s00209-016-1619-8
- language
- English
- LU publication?
- no
- id
- fcfc94d3-cadc-48f4-8745-8cd849f346fe
- date added to LUP
- 2022-03-09 15:13:59
- date last changed
- 2025-04-04 15:00:22
@article{fcfc94d3-cadc-48f4-8745-8cd849f346fe,
abstract = {{We introduce n-abelian and n-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that n-cluster-tilting subcategories of abelian (resp. exact) categories are n-abelian (resp. n-exact). These results allow to construct several examples of n-abelian and n-exact categories. Conversely, we prove that n-abelian categories satisfying certain mild assumptions can be realized as n-cluster-tilting subcategories of abelian categories. In analogy with a classical result of Happel, we show that the stable category of a Frobenius n-exact category has a natural (n+2)-angulated structure in the sense of Geiß–Keller–Oppermann. We give several examples of n-abelian and n-exact categories which have appeared in representation theory, commutative algebra, commutative and non-commutative algebraic geometry.}},
author = {{Jasso, Gustavo}},
issn = {{0025-5874}},
language = {{eng}},
number = {{3-4}},
pages = {{703--759}},
publisher = {{Springer}},
series = {{Mathematische Zeitschrift}},
title = {{<i>n</i>-abelian and <i>n</i>-exact categories}},
url = {{http://dx.doi.org/10.1007/s00209-016-1619-8}},
doi = {{10.1007/s00209-016-1619-8}},
volume = {{283}},
year = {{2016}},
}