vi CONTENTS
2. Glueing Squares and Filling Lemmas 86
3. Tensor Products and Complicial Sets 90
4. Superstructures of Complicial Sets 102
Chapter 8. The Path Category Construction 105
1. The Complicial Category of Prisms 105
2. Path Categories and Superstructures 108
3. A Complicial Double Category with Connections 110
Chapter 9. Complicial Decalage Constructions 115
1. A Decalage Construction on Complicial Sets 115
2. A Path Construction on Complicially Enriched Categories 120
3. A Decalage Construction on Complicially Enriched Categories 125
4. Semi-Simplicial Reconstruction 127
Chapter 10. Street's a;-Categorical Nerve Construction 133
1. Parity Complexes 133
2. Collapsers and Stratified Parity Complexes 147
3. u-Categorical Nerve Constructions 150
4. Products of Parity Complexes and the Complicial Tensor 155
5. An Inductive Proof of the Street-Roberts Conjecture 163
Bibliography 173
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