Some categorical properties of the algorithm of differentiation VII for equipped posets. (Q2904602)

Zavadskij's differentiation algorithms, originally developed for the representation theory of partially ordered sets, allow a kind of surgery of posets (with additional structure) to simplify the category of their indecomposables. To deal with the various problems arising in this context, Zavadskij invented a plethora of 17 differentiation algorithms of increasing sophistication, a project with unmistakable similarities to the late achievements before the temporary breakdown of invariant theory after 1900. To be sure, these developments will be revisited, maybe in a late future, to be understood in a comprising theory of arithmetic in dimension one.NEWLINENEWLINE The present paper deals with ``equipped posets'', according to representations involving quadratic field extensions. The algorithm DVII [see \textit{C. Rodríguez Beltrán} and \textit{A. G. Zavadskij}, Rev. Colomb. Mat. 41, Spec. Iss., 117-142 (2007; Zbl 1149.16014)] is analysed in a categorical fashion.