Category of Vilenkin−Kuznetsov−Smorodinsky−Smirnov Trees

Abstract

First, we briefly review the definitions and the basic properties of operads and trees. There are many useful types of operads, and each type is determined by the choice of two categories: basic symmetric monoidal category (C, □), which supports the classical linear operads, and a category of graphs Γ reflecting the combinatorics of operadic data and axioms. From this viewpoint, the specific operad is a functor Γ → C. Second, our aim is the construction of the category of Vilenkin–Kuznetsov–Smorodinsky–Smirnov (VKSS) trees, which contains VKSS-trees as objects and morphisms generated by a rotation of the n-dimensional space and transforming functions of VKSS-trees.