On a characterization of (co)silting objects

Simion Breaz

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arXiv · 2303.06843

On a characterization of (co)silting objects

Simion Breaz

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Abstract

We prove that an object $U$ in a triangulated category with coproducts is silting if and only if it is a (weak) generator of the category, the orthogonal class $U^{\perp_{>0}}$ contains $U$, and $U^{\perp_{>0}}$ is closed under direct sums. The proof can be dualized to provide a characterization for cosilting objects in triangulated categories with products.

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Simion Breaz. 2023-03-13. On a characterization of (co)silting objects. https://arxiv.org/abs/2303.06843

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