On a characterization of (co)silting objects

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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