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Complicial sets characterising the simplicial nerves of strict $\omega $-categories

About this Title

Dominic Verity

Publication: Memoirs of the American Mathematical Society
Publication Year 2008: Volume 193, Number 905
ISBNs: 978-0-8218-4142-6 (print); 978-1-4704-0511-3 (online)
MathSciNet review: 2399898
MSC: Primary 18D05; Secondary 18D15, 18D35, 18G30, 55U10

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Table of Contents


  • 1. Simplicial operators and simplicial sets
  • 2. A little categorical background
  • 3. Double categories, 2-categories and $n$-categories
  • 4. An introduction to the decalage construction
  • 5. Stratifications and filterings of simplicial sets
  • 6. Pre-complicial sets
  • 7. Complicial sets
  • 8. The path category construction
  • 9. Complicial decalage constructions
  • 10. Street’s $\omega $-categorical nerve construction