2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161182The primary purpose of this work is to characterise strict ω-categories as simplicial sets with structure. We prove the Street-Roberts conjecture which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title.167 pages, AMSLaTeX; minor revisions and typo fixes, reformatted for better A4 printingCategory TheoryAlgebraic Topology18D05, 55U10 (Primary) 18D15, 18D20, 18D35, 18F99, 18G30 (Secondary)text