Let $ \mathscr{B} $ be an extriangulated category which admits a cluster tilting subcategory $ \mathcal{T} $. We firstly introduce notions of $ \mathcal{T} $-cluster tilting subcategories and related subcategories. Then we prove there is a correspondence between $ \mathcal{T} $-cluster tilting subcategories of $ \mathscr{B} $ and support $ \tau $-tilting pairs of $ mod \underline{\Omega(\mathcal{T}}) $, which recovers several main results from the literature. Note that the generalization is nontrivial and we give a new proof technique.
Citation: Zhen Zhang, Shance Wang. Relative cluster tilting subcategories in an extriangulated category[J]. Electronic Research Archive, 2023, 31(3): 1613-1624. doi: 10.3934/era.2023083
Let $ \mathscr{B} $ be an extriangulated category which admits a cluster tilting subcategory $ \mathcal{T} $. We firstly introduce notions of $ \mathcal{T} $-cluster tilting subcategories and related subcategories. Then we prove there is a correspondence between $ \mathcal{T} $-cluster tilting subcategories of $ \mathscr{B} $ and support $ \tau $-tilting pairs of $ mod \underline{\Omega(\mathcal{T}}) $, which recovers several main results from the literature. Note that the generalization is nontrivial and we give a new proof technique.
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Zhen Zhang, Shance Wang. Relative cluster tilting subcategories in an extriangulated category[J]. Electronic Research Archive, 2023, 31(3): 1613-1624. doi: 10.3934/era.2023083
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