Grothendieck group for sequences
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
For any category with a distinguished collection of sequences, such as $n$-exangulated category, category of N-complexes and category of precomplexes, we consider its Grothendieck group and similar results of Bergh-Thaule for $n$-angulated categories \cite{bergh2014grothendieck} are proven. A classification result of dense complete subcategories is given and we give a formal definition of K-groups for these categories following Grayson's algebraic approach of K-theory for exact categories \cite{grayson2012algebraic}.
Abstract
For any category with a distinguished collection of sequences, such as $n$-exangulated category, category of N-complexes and category of precomplexes, we consider its Grothendieck group and similar results of Bergh-Thaule for $n$-angulated categories \cite{bergh2014grothendieck} are proven. A classification result of dense complete subcategories is given and we give a formal definition of K-groups for these categories following Grayson's algebraic approach of K-theory for exact categories \cite{grayson2012algebraic}.
참고문헌 (11)
- P. A. Bergh, "The Grothendieck group of an n-angulated category", J. Pure Appl. Algebra, 218(2), pp.354~366 (2014)[DOI]
- B. I. Dundas, "The local structure of algebraic K-theory" (2013), Springer-Verlag London, Ltd
- C. Geiss, "n-angulated categories", J. Reine Angew. Math, 675, pp.101~120 (2013)[DOI]
- D. R. Grayson, "Algebraic K-theory via binary complexes", J. Amer. Math. Soc, 25(4), pp.1149~1167 (2012)[DOI]
- T. Harris, "Algebraic proofs of some fundamental theorems in algebraic K-theory", Homol-ogy Homotopy Appl, 17(1), pp.267~280 (2015)[DOI]
- J. Haugland, "The Grothendieck group of an n-exangulated category", Appl. Categ. Struc-tures, 29(3), pp.431~446 (2021)[DOI]
- M. Herschend, "n-exangulated categories (I): Definitions and fundamental properties", J. Algebra, 570, pp.531~586 (2021)[DOI]
- G. Jasso, "n-Abelian and n-exact categories", Math. Z, 283(3-4), pp.703~759 (2016)[DOI]
- H. Matsui, "Classifying Dense Resolving and Coresolving Subcategories of Exact Cate-gories Via Grothendieck Groups", Algebr. Represent. Theory, 21(3), pp.551~563 (2018)[DOI]
- H. Nakaoka, "Extriangulated categories, Hovey twin cotorsion pairs and model structures", Cah. Topol. Géom. Différ. Catég, 60(2), pp.117~193 (2019)
- R. W. Thomason, "The classification of triangulated subcategories", Compos. Math, 105(1), pp.1~27 (1997)[DOI]