On a characterization of (co)silting objects

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⊥>0 contains U, and U⊥>0 is closed under direct sums. The proof can be dualized to provide a characterization for cosilting objects in triangulated categories with products.