2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165855An elementary theory of strict $\infty $-categories with application to concrete duality is given. All known famous dualities (Gelfand-Naimark, Pontryagin, Stone, etc.) are so-called natural. A criterion of existence of such a duality for higher categories is formulated. New examples are presented.It is a revision of the previous version 'Strict $\infty $-categories. Concrete Duality', 50 pagesCategory Theory18D25; 18F99text