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# 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

#### 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

Paper received on 18 July 2016.

Revised paper received on 15 December 2016.