TL;DR
This paper explores the symmetry in recollements of triangulated categories with Serre functors, showing how the roles of subcategories S and U can be interchanged under certain conditions.
Contribution
It demonstrates the interchangeability of subcategories in recollements of triangulated categories possessing Serre functors, revealing a new symmetry property.
Findings
S and U can be interchanged in recollements with Serre functors
Recollement symmetry depends on the existence of a Serre functor
Enhanced understanding of triangulated category structures
Abstract
A recollement describes one triangulated category T as "glued together" from two others, S and U. The definition is not symmetrical in S and U, but this note shows how S and U can be interchanged when T has a Serre functor.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Logic, programming, and type systems