Abstract
Let ( C , E , s ) be an extriangulated category with a proper class ξ of E -triangles. In this paper, we study Gorenstein derived functors for extriangulated categories. More precisely, we first introduce the notion of the proper ξ ‐ G projective resolution for an object in C and define the functors ξ xt G P ( ξ ) and ξ xt G I ( ξ ) . Under some assumptions, we give some equivalent characterizations for ξ ‐ G projective and ξ ‐ G injective dimensions of objects in C by vanishing of such functors. As an application, our main results generalize Ren and Liu’s work. Moreover, our proof is not far from the usual module categories or triangulated categories.
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
