2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70439We propose a recursive definition of V-n-categories and their morphisms. We show that for V k-fold monoidal the structure of a (k-n)-fold monoidal strict (n+1)-category is possessed by V-n-Cat. This article is a completion of the work begun in math.CT/0306086, and the initial sections duplicate the beginning of that paper.31 pages; Completes the program begun in Higher Dimensional Enrichment, preprint math.CT/0306086Category TheoryAlgebraic TopologyQuantum Algebra18D10; 18D20text