Abstract

Let A be an abelian category and C an additive full subcategory of A. We provide a method to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short exact sequence in A from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category G(C) posed by Sather-Wagstaff, Sharif and White; and also prove that G(C) is closed under direct summands. In addition, we obtain some criteria for computing the C-dimension and the G(C)-dimension of an object in A.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call