外三角范畴粘合的低阶K－群

Lower K－groups of the recollement of extriangulated categories

摘要

证明在一定条件下外三角范畴左（右）粘合中 3 个范畴的K_i－群间具有直和同构关系，推广关于 Abel 范畴（三角范畴）粘合的K_i－群的已有结论（i=0,1）。利用外三角范畴的粘合刻画 3 个范畴的幂等完备化范畴K_i－群的可加性（i=0,1）。

Abstract

This paper proves that，under certain conditions，there exists the direct and isomorphic relation among the K_i－groups of three categories in the left（right）recollement of extriangulated categories，which generalizes the conclusions of K_i－groups of recol－ lements of abelian（triangulated）categories (i=0,1) ．The recollement of extriangulated categories is used to describe the additivity of K_i－groups of the idempotent completion categories of its three categories (i=0,1) ．

关键词

外三角范畴 / 粘合 / K_i－群 / 幂等完备化范畴 / 三角范畴

Key words

extriangulated category / recollement / K_i－group / idempotent completion category / triangulated category

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基金资助

国家自然科学基金资助项目(11871404)

福建江夏学院国家基金培育项目(JXZ2023005)