2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63028We give a brief account of a construction called tokens here, which is significant in algebra, analysis, combinatorics, and physics. Tokens allow to express a semigroup on one set via a semigroup convolution on another set. Therefore tokens are similar to intertwining operators but are more flexible. Keywords: semigroups, hypergroups, tokens, poset, multiplicative functions, polynomial sequence of binomial type, integral kernel, wavelets, refinement equation, special functions, quantum propagator, path integral, quantum computing.LaTeX, 10 pages, 3 PS figuresFunctional AnalysisMathematical PhysicsCombinatorics43A20, 05A40, 81S40text