Lifting and restricting recollement data
The paper continues the authors' study of recollement data for triangulated categories with a generator [\textit{P. Nicolás} and \textit{M. Saorín}, J. Algebra 322, No.~4, 1220--1250 (2009; Zbl 1187.18008)]. In 1991, \textit{S.~König} gave a criterion for the bounded above derived category of a module category to be obtainable as a recollement. The present paper relates theorems of that type with unbounded analogues. The authors define the right bounded derived category \(D^-\mathcal A\) of a differential graded category \(\mathcal A\) to be the union of the aisles of the canonical t-structures of \(D\mathcal A\). They give a criterion for \(D^-\mathcal A\) to be a recollement of right bounded derived categories of the same type. They specialize this result to the case of dg-categories with cohomology concentrated in non-negative degrees, and also to the setting of König's theorem.
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