Abstract
In this paper, we prove that if a triangulated category \( \mathcal{D} \) admits a recollement relative to triangulated categories \( \mathcal{D}' \) and \( \mathcal{D}'' \), then the abelian category \( \mathcal{D}/\mathcal{T} \) admits a recollement relative to abelian categories \( \mathcal{D}'/i*(\mathcal{T}) \) and \( \mathcal{D}''/j*(\mathcal{T}) \) where \( \mathcal{T} \) is a cluster tilting subcategory of \( \mathcal{D} \) and satisfies \( i_* i^* (\mathcal{T}) \subset \mathcal{T},j_* j^* (\mathcal{T}) \subset \mathcal{T} \).
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Lin, Y., Wang, M. From recollement of triangulated categories to recollement of abelian categories. Sci. China Math. 53, 1111–1116 (2010). https://doi.org/10.1007/s11425-009-0189-1
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DOI: https://doi.org/10.1007/s11425-009-0189-1