Geodesic
Relative Auslander bijection in $n$-exangulated categories
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 525-552
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The aim of this article is to study the relative Auslander bijection in \hbox {$n$-exangulated} categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
The aim of this article is to study the relative Auslander bijection in \hbox {$n$-exangulated} categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
DOI : 10.21136/CMJ.2023.0127-22
Classification : 16G70, 18E10, 18G80
Keywords: $n$-exangulated category; generalized Auslander-Reiten-Serre duality; restricted Auslander bijection 
@article{10_21136_CMJ_2023_0127_22,
     author = {He, Jian and He, Jing and Zhou, Panyue},
     title = {Relative {Auslander} bijection in $n$-exangulated categories},
     journal = {Czechoslovak Mathematical Journal},
     pages = {525--552},
     year = {2023},
     volume = {73},
     number = {2},
     doi = {10.21136/CMJ.2023.0127-22},
     mrnumber = {4586909},
     zbl = {07729522},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0127-22/}
}
TY  - JOUR
AU  - He, Jian
AU  - He, Jing
AU  - Zhou, Panyue
TI  - Relative Auslander bijection in $n$-exangulated categories
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 525
EP  - 552
VL  - 73
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0127-22/
DO  - 10.21136/CMJ.2023.0127-22
LA  - en
ID  - 10_21136_CMJ_2023_0127_22
ER  - 
%0 Journal Article
%A He, Jian
%A He, Jing
%A Zhou, Panyue
%T Relative Auslander bijection in $n$-exangulated categories
%J Czechoslovak Mathematical Journal
%D 2023
%P 525-552
%V 73
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0127-22/
%R 10.21136/CMJ.2023.0127-22
%G en
%F 10_21136_CMJ_2023_0127_22
He, Jian; He, Jing; Zhou, Panyue. Relative Auslander bijection in $n$-exangulated categories. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 525-552. doi: 10.21136/CMJ.2023.0127-22

[1] Auslander, M.: Functors and morphisms determined by objects. Representation Theory of Algebras Lecture Notes in Pure Applied Mathematics 37. Marcel Dekker, New York (1978), 1-244. | MR | JFM

[2] Auslander, M., Reiten, I.: Representation theory of Artin algebras. III: Almost split sequences. Commun. Algebra 3 (1975), 239-294. | DOI | MR | JFM

[3] Auslander, M., Reiten, I.: Representation theory of Artin algebras. IV: Invariants given by almost split sequences. Commun. Algebra 5 (1977), 443-518. | DOI | MR | JFM

[4] Chen, X.-W.: The Auslander bijections and universal extensions. Ark. Mat. 55 (2017), 41-59. | DOI | MR | JFM

[5] Dräxler, P., Reiten, I., Smalø, S. O., Solberg, Ø.: Exact categories and vector space categories. Trans. Am. Math. Soc. 351 (1999), 647-682. | DOI | MR | JFM

[6] Geiss, C., Keller, B., Oppermann, S.: $n$-angulated categories. J. Reine Angew. Math. 675 (2013), 101-120. | DOI | MR | JFM

[7] He, J., He, J., Zhou, P.: Auslander-Reiten-Serre duality for $n$-exangulated categories. Available at , 24 pages. | arXiv

[8] He, J., He, J., Zhou, P.: Higher Auslander-Reiten sequences via morphisms determined by objects. Available at , 28 pages. | arXiv | MR

[9] He, J., Hu, J., Zhang, D., Zhou, P.: On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories. Ark. Mat. 60 (2022), 365-385. | DOI | MR | JFM

[10] He, J., Zhou, P.: $n$-exact categories arising from $n$-exangulated categories. Available at , 16 pages. | arXiv

[11] Herschend, M., Liu, Y., Nakaoka, H.: $n$-exangulated categories. I: Definitions and fundamental properties. J. Algebra 570 (2021), 531-586. | DOI | MR | JFM

[12] Herschend, M., Liu, Y., Nakaoka, H.: $n$-exangulated categories. II: Constructions from $n$-cluster tilting subcategories. J. Algebra 594 (2022), 636-684. | DOI | MR | JFM

[13] Hu, J., Zhang, D., Zhou, P.: Two new classes of $n$-exangulated categories. J. Algebra 568 (2021), 1-21. | DOI | MR | JFM

[14] Iyama, O., Nakaoka, H., Palu, Y.: Auslander-Reiten theory in extriangulated categories. Available at , 40 pages. | arXiv

[15] Jasso, G.: $n$-abelian and $n$-exact categories. Math. Z. 283 (2016), 703-759. | DOI | MR | JFM

[16] Jiao, P.: The generalized Auslander-Reiten duality on an exact category. J. Algebra Appl. 17 (2018), Article ID 1850227, 14 pages. | DOI | MR | JFM

[17] Jiao, P.: Auslander's defect formula and a commutative triangle in an exact category. Front. Math. China 15 (2020), 115-125. | DOI | MR | JFM

[18] Liu, Y., Zhou, P.: Frobenius $n$-exangulated categories. J. Algebra 559 (2020), 161-183. | DOI | MR | JFM

[19] Nakaoka, H., Palu, Y.: Extriangulated categories, Hovey twin cotorsion pairs and model structures. Cah. Topol. Géom. Différ. Catég. 60 (2019), 117-193. | MR | JFM

[20] Ringel, C. M.: The Auslander bijections: How morphisms are determined by modules. Bull. Math. Sci. 3 (2013), 409-484. | DOI | MR | JFM

[21] Zhao, T.: Relative Auslander bijection in extriangulated categories. Available at www.researchgate.net/publication/367217942 (2021). | MR

[22] Zhao, T., Tan, L., Huang, Z.: Almost split triangles and morphisms determined by objects in extriangulated categories. J. Algebra 559 (2020), 346-378. | DOI | MR | JFM

[23] Zhao, T., Tan, L., Huang, Z.: A bijection triangle in extriangulated categories. J. Algebra 574 (2021), 117-153. | DOI | MR | JFM

[24] Zheng, Q., Wei, J.: $(n+2)$-angulated quotient categories. Algebra Colloq. 26 (2019), 689-720. | DOI | MR | JFM

Cité par Sources :