Complicial Sets Characterising the Simplicial Nerves of Strict Omega-Categories

The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ""complicial sets"" defined and named by John Roberts in his handwritten notes of that title (circa 1978).