A note on the axioms for n-angulated categories
In this paper, we discuss the axioms for an n-angulated category, which is introduced by Geiss, Keller and Oppermann in [3]. We improve a result of Bergh and Thaule [2], which gives equivalent axioms for a pre-n-angulated category. Moreover, we generalize a result of Neeman's [9] to n-angulated...
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| Published in | Journal of algebra Vol. 636; pp. 279 - 296 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.12.2023
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-8693 1090-266X |
| DOI | 10.1016/j.jalgebra.2023.08.011 |
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| Abstract | In this paper, we discuss the axioms for an n-angulated category, which is introduced by Geiss, Keller and Oppermann in [3]. We improve a result of Bergh and Thaule [2], which gives equivalent axioms for a pre-n-angulated category. Moreover, we generalize a result of Neeman's [9] to n-angulated categories, which gives a sufficient and necessary condition for an n-angulated functor having an adjoint. |
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| AbstractList | In this paper, we discuss the axioms for an n-angulated category, which is introduced by Geiss, Keller and Oppermann in [3]. We improve a result of Bergh and Thaule [2], which gives equivalent axioms for a pre-n-angulated category. Moreover, we generalize a result of Neeman's [9] to n-angulated categories, which gives a sufficient and necessary condition for an n-angulated functor having an adjoint. |
| Author | Shi, Xuechen Xu, Jinde |
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| References | Mitchell (br0090) 1965; vol. XVII Bergh, Thaule (br0020) 2013; 13 Arentz-Hansen, Bergh, Thaule (br0010) 2016; 31 Assem, Simson, Skowroński (br0050) 2006; vol. 65 Geiss, Keller, Oppermann (br0030) 2013; 675 Freyd (br0060) 1966 Happel (br0080) 1988; vol. 119 Neeman (br0100) 2001; vol. 148 Freyd (br0070) 1966 Freyd (10.1016/j.jalgebra.2023.08.011_br0070) 1966 Geiss (10.1016/j.jalgebra.2023.08.011_br0030) 2013; 675 Assem (10.1016/j.jalgebra.2023.08.011_br0050) 2006; vol. 65 Freyd (10.1016/j.jalgebra.2023.08.011_br0060) 1966 Bergh (10.1016/j.jalgebra.2023.08.011_br0020) 2013; 13 Neeman (10.1016/j.jalgebra.2023.08.011_br0100) 2001; vol. 148 Mitchell (10.1016/j.jalgebra.2023.08.011_br0090) 1965; vol. XVII Happel (10.1016/j.jalgebra.2023.08.011_br0080) 1988; vol. 119 Arentz-Hansen (10.1016/j.jalgebra.2023.08.011_br0010) 2016; 31 |
| References_xml | – volume: vol. 65 year: 2006 ident: br0050 article-title: Elements of the Representation Theory of Associative Algebras, vol. 1. Techniques of Representation Theory publication-title: London Mathematical Society Student Texts – volume: vol. 148 year: 2001 ident: br0100 article-title: Triangulated Categories publication-title: Ann. Math. Studies – volume: 31 start-page: 477 year: 2016 end-page: 483 ident: br0010 article-title: The morphism axiom for n-angulated categories publication-title: Theory Appl. Categ. – volume: vol. XVII year: 1965 ident: br0090 article-title: Theory of Categories publication-title: Pure and Applied Math. – volume: 13 start-page: 2405 year: 2013 end-page: 2428 ident: br0020 article-title: The axioms for n-angulated categories publication-title: Algebraic Geom. Topol. – volume: 675 start-page: 101 year: 2013 end-page: 120 ident: br0030 article-title: n-angulated categories publication-title: J. Reine Angew. Math. – volume: vol. 119 year: 1988 ident: br0080 article-title: Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras publication-title: London Mathematical Society Lecture Note Series – start-page: 121 year: 1966 end-page: 172 ident: br0070 article-title: Stable homotopy publication-title: Proc. Conf. Categorical Algebra – start-page: 95 year: 1966 end-page: 120 ident: br0060 article-title: Representations in abelian categories publication-title: Proc. Conf. Categorical Algebra – volume: 31 start-page: 477 year: 2016 ident: 10.1016/j.jalgebra.2023.08.011_br0010 article-title: The morphism axiom for n-angulated categories publication-title: Theory Appl. Categ. – start-page: 121 year: 1966 ident: 10.1016/j.jalgebra.2023.08.011_br0070 article-title: Stable homotopy – volume: 13 start-page: 2405 year: 2013 ident: 10.1016/j.jalgebra.2023.08.011_br0020 article-title: The axioms for n-angulated categories publication-title: Algebraic Geom. Topol. doi: 10.2140/agt.2013.13.2405 – volume: vol. 119 year: 1988 ident: 10.1016/j.jalgebra.2023.08.011_br0080 article-title: Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras – start-page: 95 year: 1966 ident: 10.1016/j.jalgebra.2023.08.011_br0060 article-title: Representations in abelian categories – volume: vol. 65 year: 2006 ident: 10.1016/j.jalgebra.2023.08.011_br0050 article-title: Elements of the Representation Theory of Associative Algebras, vol. 1. Techniques of Representation Theory – volume: vol. XVII year: 1965 ident: 10.1016/j.jalgebra.2023.08.011_br0090 article-title: Theory of Categories – volume: vol. 148 year: 2001 ident: 10.1016/j.jalgebra.2023.08.011_br0100 article-title: Triangulated Categories – volume: 675 start-page: 101 year: 2013 ident: 10.1016/j.jalgebra.2023.08.011_br0030 article-title: n-angulated categories publication-title: J. Reine Angew. Math. |
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| Snippet | In this paper, we discuss the axioms for an n-angulated category, which is introduced by Geiss, Keller and Oppermann in [3]. We improve a result of Bergh and... |
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| Title | A note on the axioms for n-angulated categories |
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