The Related Researches On Monomorphism Categories Of N-th Differential Objects And Morita Algebras

This is a dissertation on monomorphism category of n-th differential objects and Morita algebras.In the first part,we mainly study the related research and stable category of the monomorphism category of n-th differential objects,and mainly characterize the torsion differential modules on path algebras.Given the Abelian category C and the category of its n-th differential object C[?]n,we use the adjoint pair to characterize the relationship between their silting objects.In particular,if C is a Frobenius category,We denote the stable monomorphism category of C and C[?]n by Mon(C)and Mon(C[?]n)respectively.In the second part,we mainly study the monomorphism category on Morita context algebras,given A and B and two bimodules ANB and BMA satisfying M(?)AN=0=N(?)BM,let ?=(?)be Morita context algebras.We introduce and study the monomorphism category M(A,M,N,B)of ? and its dual epimorphism category ?(A,M,N,B).We give the characterization of M(A,M,N,B)by using the left perpendicular category of cotilting modules,and give the Ringel-Schmidmeier-Simson equivalence.