# Complicial Sets Characterising the Simplicial Nerves of Strict omega-Categories

American Mathematical Soc., 2008 - 184 pages
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).

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### Table des matières

 Chapter 1 Simplicial Operators and Simplicial Sets 1 Chapter 2 A Little Categorical Background 21 Chapter 3 Double Categories 2Categories and nCategories 33 Chapter 4 An Introduction to the Decalage Construction 47 Chapter 5 Stratifications and Filterings of Simplicial Sets 55 Chapter 6 PreComplicial Sets 65
 Chapter 7 Complicial Sets 85 Chapter 8 The Path Category Construction 105 Chapter 9 Complicial Decalage Constructions 115 Chapter 10 Streets ωCategorical Nerve Construction 133 Bibliography 173 Droits d'auteur