Balance of complete cohomology in extriangulated categories
Abstract
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. In this paper, we study the balance of complete cohomology in $(\mathcal{C},\mathbb{E},\mathfrak{s})$, which is motivated by a result of Nucinkis that complete cohomology of modules is not balanced in the way the absolute cohomology Ext is balanced. As an application, we give some criteria for identifying a triangulated catgory to be Gorenstein and an artin algebra to be $F$-Gorenstein.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.13711
- arXiv:
- arXiv:2004.13711
- Bibcode:
- 2020arXiv200413711H
- Keywords:
-
- Mathematics - Category Theory;
- Mathematics - Rings and Algebras;
- 18E30;
- 18E10;
- 18G25;
- 55N20
- E-Print:
- 18 pages. arXiv admin note: text overlap with arXiv:2003.11852, arXiv:1908.00931