Homology, Homotopy and Applications
Volume 19 (2017)
A note on thick subcategories and wide subcategories
Pages: 131 – 139
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.
wide subcategory, lattice isomorphism, hereditary algebra
2010 Mathematics Subject Classification
16E05, 16G20, 18E30
Paper received on 18 July 2016.
Revised paper received on 15 December 2016.