Let l be a Krull-Schmidt n-exangulated category and A be an n-extension closed subcategory of l.Then A inherits the n-exangulated structure from the given n-exangulated category in a natural way.This construction give...Let l be a Krull-Schmidt n-exangulated category and A be an n-extension closed subcategory of l.Then A inherits the n-exangulated structure from the given n-exangulated category in a natural way.This construction gives n-exangulated categories which are neither n-exact categories in the sense of Jasso nor(n+2)-angulated categories in the sense of Geiss-Keller-Oppermann in general.Furthermore,we also give a sufficient condition on when an n-exangulated category A is an n-exact category.These results generalize work by Klapproth and Zhou.展开更多
The notion of D-mutation pairs of subcategories in an n-exangulated category is defined in this article.When(Z,Z)is a P-mutation pair in an n-exangulated category(C,E,s),the quotient category Z/Dcarries naturally an(n...The notion of D-mutation pairs of subcategories in an n-exangulated category is defined in this article.When(Z,Z)is a P-mutation pair in an n-exangulated category(C,E,s),the quotient category Z/Dcarries naturally an(n+2)-angulated structure.This result generalizes a theorem of Zhou and Zhu for extriangulated categories.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12171230)supported by the Hunan Provincial Natural Science Foundation of China(Grant No.2023JJ30008)。
文摘Let l be a Krull-Schmidt n-exangulated category and A be an n-extension closed subcategory of l.Then A inherits the n-exangulated structure from the given n-exangulated category in a natural way.This construction gives n-exangulated categories which are neither n-exact categories in the sense of Jasso nor(n+2)-angulated categories in the sense of Geiss-Keller-Oppermann in general.Furthermore,we also give a sufficient condition on when an n-exangulated category A is an n-exact category.These results generalize work by Klapproth and Zhou.
基金Supported by the National Natural Science Foundation of China(Grant No.11771212)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘The notion of D-mutation pairs of subcategories in an n-exangulated category is defined in this article.When(Z,Z)is a P-mutation pair in an n-exangulated category(C,E,s),the quotient category Z/Dcarries naturally an(n+2)-angulated structure.This result generalizes a theorem of Zhou and Zhu for extriangulated categories.
