Complicial Sets Characterising the Simplicial Nerves of Strict \(𝜔\)-Categories
Share this pageDominic Verity
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).
On the way the author substantially
develops Roberts' theory of complicial sets itself and makes
contributions to Street's theory of parity complexes. In particular,
he studies a new monoidal closed structure on the category of
complicial sets which he shows to be the appropriate generalisation
of the (lax) Gray tensor product of 2-categories to this
context. Under Street's \(\omega\)-categorical nerve
construction, which the author shows to be an equivalence, this tensor product
coincides with those of Steiner, Crans and others.
Table of Contents
Table of Contents
Complicial Sets Characterising the Simplicial Nerves of Strict $$-Categories
- Contents v6 free
- Preface ix10 free
- Chapter 1. Simplicial Operators and Simplicial Sets 118 free
- Chapter 2. A Little Categorical Background 2138
- Chapter 3. Double Categories, 2-Categories and n-Categories 3350
- Chapter 4. An Introduction to the Decalage Construction 4764
- Chapter 5. Stratifications and Filterings of Simplicial Sets 5572
- Chapter 6. Pre-Complicial Sets 6582
- Chapter 7. Complicial Sets 85102
- Chapter 8. The Path Category Construction 105122
- Chapter 9. Complicial Decalage Constructions 115132
- Chapter 10. Street's ω-Categorical Nerve Construction 133150
- Bibliography 173190