Categorical properties of some algorithms of differentiation for equipped posets

Abstract

In this paper it is proved that the algorithms of differentiation VIII-X (introduced by A.G. Zavadskij to classify equipped posets of tame representation type) induce categorical equivalences between some quotient categories, in particular, an algorithm \(A_{z}\) is introduced to build equipped posets with a pair of points \((a, b)\) suitable for differentiation VII such that the subset of strong points related with the weak point \(a\) is not empty.