Homology, Homotopy and Applications

Volume 19 (2017)

Number 2

A note on thick subcategories and wide subcategories

Pages: 131 – 139

DOI: http://dx.doi.org/10.4310/HHA.2017.v19.n2.a8

Authors

Chao Zhang (Department of Mathematics, Guizhou University, Guiyang, China)

Hongyan Cai (Department of Mathematics, Guizhou University, Guiyang, China)

Abstract

For a triangulated category with a bounded t-structure, we prove that there is a bijection between wide subcategories of its heart and thick subcategories of the triangulated category which are closed under the corresponding cohomological functor. We prove that a finite-dimensional triangular algebra over an algebraically closed field is hereditary if and only if any thick subcategory of the bounded derived category is closed under the usual cohomological functor.

Keywords

wide subcategory, lattice isomorphism, hereditary algebra

2010 Mathematics Subject Classification

16E05, 16G20, 18E30

Full Text (PDF format)

Received 18 July 2016

Received revised 15 December 2016

Published 18 October 2017