Semisimple category
= Semisimple category
In the finite-dimensional setting, a semisimple category is an <additive category> over a <field> in which every object is a finite <biproduct> of simple objects, different simple objects have zero <morphism> spaces, and the <endomorphism> algebra of each simple object is a <division algebra>. Such categories have finite <matrix> blocks and all their <idempotents> split. The <semisimplicity of the reduced Temperley-Lieb category> gives an example whose simple objects are the surviving <Jones-Wenzl colors>.