Institute of Mathematics

References:
[1] M. Auslander: 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 0480688 | Zbl 0383.16015
[2] M. Auslander, I. Reiten: Representation theory of Artin algebras. III: Almost split sequences. Commun. Algebra 3 (1975), 239-294. DOI 10.1080/00927877508822046 | MR 0379599 | Zbl 0331.16027
[3] M. Auslander, I. Reiten: Representation theory of Artin algebras. IV: Invariants given by almost split sequences. Commun. Algebra 5 (1977), 443-518. DOI 10.1080/00927877708822180 | MR 0439881 | Zbl 0396.16007
[4] X.-W. Chen: The Auslander bijections and universal extensions. Ark. Mat. 55 (2017), 41-59. DOI 10.4310/ARKIV.2017.v55.n1.a2 | MR 3711141 | Zbl 1388.16018
[5] P. Dräxler, I. Reiten, S. O. Smalø, Ø. Solberg: Exact categories and vector space categories. Trans. Am. Math. Soc. 351 (1999), 647-682. DOI 10.1090/S0002-9947-99-02322-3 | MR 1608305 | Zbl 0916.16002
[6] C. Geiss, B. Keller, S. Oppermann: $n$-angulated categories. J. Reine Angew. Math. 675 (2013), 101-120. DOI 10.1515/CRELLE.2011.177 | MR 3021448 | Zbl 1271.18013
[7] J. He, J. He, P. Zhou: Auslander-Reiten-Serre duality for $n$-exangulated categories. Available at https://arxiv.org/abs/2112.00981 (2021), 24 pages.
[8] J. He, J. He, P. Zhou: Higher Auslander-Reiten sequences via morphisms determined by objects. Available at https://arxiv.org/abs/2111.06522 (2021), 28 pages.
[9] J. He, J. Hu, D. Zhang, P. Zhou: On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories. Ark. Mat. 60 (2022), 365-385. DOI 10.4310/ARKIV.2022.v60.n2.a8 | MR 4500371 | Zbl 7610639
[10] J. He, P. Zhou: $n$-exact categories arising from $n$-exangulated categories. Available at https://arxiv.org/abs/2109.12954 (2021), 16 pages.
[11] M. Herschend, Y. Liu, H. Nakaoka: $n$-exangulated categories. I: Definitions and fundamental properties. J. Algebra 570 (2021), 531-586. DOI 10.1016/j.jalgebra.2020.11.017 | MR 4188310 | Zbl 07290700
[12] M. Herschend, Y. Liu, H. Nakaoka: $n$-exangulated categories. II: Constructions from $n$-cluster tilting subcategories. J. Algebra 594 (2022), 636-684. DOI 10.1016/j.jalgebra.2021.11.042 | MR 4355116 | Zbl 07459388
[13] J. Hu, D. Zhang, P. Zhou: Two new classes of $n$-exangulated categories. J. Algebra 568 (2021), 1-21. DOI 10.1016/j.jalgebra.2020.09.041 | MR 4166049 | Zbl 1458.18006
[14] O. Iyama, H. Nakaoka, Y. Palu: Auslander-Reiten theory in extriangulated categories. Available at https://arxiv.org/abs/1805.03776v2 (2019), 40 pages.
[15] G. Jasso: $n$-abelian and $n$-exact categories. Math. Z. 283 (2016), 703-759. DOI 10.1007/s00209-016-1619-8 | MR 3519980 | Zbl 1356.18005
[16] P. Jiao: The generalized Auslander-Reiten duality on an exact category. J. Algebra Appl. 17 (2018), Article ID 1850227, 14 pages. DOI 10.1142/S0219498818502274 | MR 3895199 | Zbl 1407.16014
[17] P. Jiao: Auslander's defect formula and a commutative triangle in an exact category. Front. Math. China 15 (2020), 115-125. DOI 10.1007/s11464-020-0814-4 | MR 4074348 | Zbl 1457.16014
[18] Y. Liu, P. Zhou: Frobenius $n$-exangulated categories. J. Algebra 559 (2020), 161-183. DOI 10.1016/j.jalgebra.2020.03.036 | MR 4096714 | Zbl 1448.18022
[19] H. Nakaoka, Y. Palu: Extriangulated categories, Hovey twin cotorsion pairs and model structures. Cah. Topol. Géom. Différ. Catég. 60 (2019), 117-193. MR 3931945 | Zbl 1451.18021
[20] C. M. Ringel: The Auslander bijections: How morphisms are determined by modules. Bull. Math. Sci. 3 (2013), 409-484. DOI 10.1007/s13373-013-0042-2 | MR 3128038 | Zbl 1405.16030
[21] T. Zhao: Relative Auslander bijection in extriangulated categories. Available at www.researchgate.net/publication/367217942 (2021).
[22] T. Zhao, L. Tan, Z. Huang: Almost split triangles and morphisms determined by objects in extriangulated categories. J. Algebra 559 (2020), 346-378. DOI 10.1016/j.jalgebra.2020.04.021 | MR 4097908 | Zbl 1440.18024
[23] T. Zhao, L. Tan, Z. Huang: A bijection triangle in extriangulated categories. J. Algebra 574 (2021), 117-153. DOI 10.1016/j.jalgebra.2020.12.043 | MR 4210995 | Zbl 1459.18007
[24] Q. Zheng, J. Wei: $(n+2)$-angulated quotient categories. Algebra Colloq. 26 (2019), 689-720. DOI 10.1142/S1005386719000506 | MR 4032973 | Zbl 1427.18006