Silting Objects over the Stable Monomorphism Categoryof Higher Differential Objects

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 C and C[e](n). The partial silting properties between an abelian category C and C[e](n) are transferred, and if moreover, C is Frobenius, the partial silting objects of the stable monomorphism categories of C[e](n) are constructed from those of C.