Abstract
Higher differential objects are investigated and used for addressing three general problems. Torsionless differential modules over path algebras are characterized. The adjoint triples between triangulated categories, involving derived categories and singularity categories, are allowed to be constructed from those between the abelian categories [Formula: see text] and [Formula: see text]. The partial silting properties between an abelian category [Formula: see text] and [Formula: see text] are transferred, and if moreover,[Formula: see text] is Frobenius, the partial silting objects of the stable monomorphism categories of [Formula: see text] are constructed from those of [Formula: see text].
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