Complicial sets characterising the simplical nerves of strict [omega]-categories / / Dominic Verity

• Record Nr.: UNINA9910788852403321
• Autore: Verity Dominic <1966->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• ISBN: 1-4704-0511-3
• Descrizione fisica: 1 online resource (184 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 905
• Disciplina: 512/.62
• Soggetti: Categories (Mathematics); Algebraic topology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "May 2008, volume 193, number 905 (end of volume)."
• Nota di bibliografia: Includes bibliographical references (pages 173-174) and indexes.
• Nota di contenuto: ""Contents""; ""Preface""; ""Historical Background""; ""Relationships to Other Work""; ""Overview and Structure""; ""Chapter 1. Simplicial Operators and Simplicial Sets""; ""1. Simplicial Operators""; ""2. The Algebraist's Î? and 2-Categories""; ""3. The Algebraist's Î? and Monoidal Categories""; ""4. Simplicial Sets""; ""5. Semi- Simplicial Sets""; ""6. Analysing Products of Simplicial Sets-the Theory of Shuffles""; ""Chapter 2. A Little Categorical Background""; ""1. Reflective Full Subcategories""; ""2. LFP-Categories and LE-Theories""; ""Chapter 3. Double Categories, 2-Categories and n-Categories""""1. Categories in the Small""; ""2. Double Categories""; ""3. 2-Categories and Double Categories with Connections""; ""4. n-Categories and Ï?-Categories""; ""Chapter 4. An Introduction to the Decalage Construction""; ""1. Nerves and Decalage""; ""2. Comonad Transformations and Simplicial Reconstruction""; ""Chapter 5. Stratifications and Filterings of Simplicial Sets""; ""1. Stratified Simplicial Sets""; ""2. Superstructures and Filtered Semi- Simplicial Sets""; ""Chapter 6. Pre-Complicial Sets ""; ""1. Introducing Pre- Complicial Sets""""2. Tensor Products of Pre- Complicial Sets""; ""3. Pre- Tensors and Preservation of t- Extensions""; ""4. Some Other Preservation Properties""; ""5. A Monoidal Biclosed Structure on Pre- Complicial sets""; ""6. Superstructures of Pre-; Complicial Sets""; ""Chapter 7. Complicial Sets""; ""1. Introducing Complicial Sets""; ""2. Glueing Squares and Filling Lemmas""; ""3. Tensor Products and Complicial Sets""; ""4. Superstructures of Complicial Sets""; ""Chapter 8. The Path Category Construction""; ""1. The Complicial Category of Prisms""; ""2. Path Categories and Superstructures""""3. A Complicial Double Category with Connections""; ""Chapter 9. Complicial Decalage Constructions""; ""1. A Decalage Construction on Complicial Sets""; ""2. A Path Construction on Complicially Enriched Categories""; ""3. A Decalage Construction on Complicially Enriched Categories""; ""4. Semi-Simplicial Reconstruction""; ""Chapter 10. Street's Ï?-Categorical Nerve Construction""; ""1. Parity Complexes""; ""2. Collapsers and Stratified Parity Complexes""; ""3. Ï?-Categorical Nerve Constructions""; ""4. Products of Parity Complexes and the Complicial Tensor""""5. An Inductive Proof of the Street-Roberts Conjecture""; ""Bibliography""