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
首先,利用基于边界域粗糙近似算子,给出 n 阶边界集的定义,引入 n 阶粗糙近似算子的定义,构造粗糙集理论的一套阶梯式近似方法.然后,通过实例和相关证明表明,无论二元关系还是在覆盖环境中,总存在正整数 n ,对于任意对象集, n 阶上下近...首先,利用基于边界域粗糙近似算子,给出 n 阶边界集的定义,引入 n 阶粗糙近似算子的定义,构造粗糙集理论的一套阶梯式近似方法.然后,通过实例和相关证明表明,无论二元关系还是在覆盖环境中,总存在正整数 n ,对于任意对象集, n 阶上下近似集完全等于该对象集,即该对象集是此意义下的精确集,或其 n 阶上下近似集趋近于某一固定的对象集,即 n 阶粗糙集总能使对象集合趋近于它本身或某一固定的集合.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.
文摘首先,利用基于边界域粗糙近似算子,给出 n 阶边界集的定义,引入 n 阶粗糙近似算子的定义,构造粗糙集理论的一套阶梯式近似方法.然后,通过实例和相关证明表明,无论二元关系还是在覆盖环境中,总存在正整数 n ,对于任意对象集, n 阶上下近似集完全等于该对象集,即该对象集是此意义下的精确集,或其 n 阶上下近似集趋近于某一固定的对象集,即 n 阶粗糙集总能使对象集合趋近于它本身或某一固定的集合.
