s-Recollements and its localization
Yonggang Hu, Panyue Zhou
TL;DR
This paper introduces s-recollements as a unifying concept for various types of recollements in category theory, exploring their properties and how localization can produce recollements of triangulated categories.
Contribution
It generalizes existing recollement concepts to extriangulated categories and develops a localization method to derive triangulated recollements from s-recollements.
Findings
s-Recollements unify recollements across different categories.
Basic properties of s-recollements are established.
A method to obtain triangulated recollements via localization is provided.
Abstract
We introduce a new concept of s-recollements of extriangulated categories, which generalizes recollements of abelian categories, recollements of triangulated categories, as well as recollements of extriangulated categories. Moreover, some basic properties of s-recollements are presented. We also discuss the behavior of the localization theory on the adjoint pair of exact functors. Finally, we provide a method to obtain a recollement of triangulated categories from s-recollements of extriangulated categories via the localization theory.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra