The Extension Dimension of Subcategories and Recollements of Abelian Categories

We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements. Let Lambda', Lambda, Lambda '' be artin algebras such that (mod Lambda', mod Lambda, mod Lambda '') is a recollement, and let D' and D '' be subcategories of mod Lambda' and mod Lambda '' respectively. For any n, m >= 0, under some conditions, we get dim Omega(k) (D) <= dim Omega(n)(D')+ dim Omega(m) (D '')+ 1, where k = max{m, n} and D is the subcategory of mod. glued by D' and D ''; moreover, we give a sufficient condition such that the converse inequality holds true. As applications, some results for Igusa-Todorov subcategories and syzygy finite subcategories are obtained.