04213nam 2200589 450 991078885240332120170822144147.01-4704-0511-3(CKB)3360000000465089(EBL)3114196(SSID)ssj0000888843(PQKBManifestationID)11492664(PQKBTitleCode)TC0000888843(PQKBWorkID)10867690(PQKB)11481256(MiAaPQ)EBC3114196(RPAM)15141574(PPN)195417941(EXLCZ)99336000000046508920080114h20082008 uy| 0engur|n|---|||||txtccrComplicial sets characterising the simplical nerves of strict [omega]-categories /Dominic VerityProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (184 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 905"May 2008, volume 193, number 905 (end of volume)."0-8218-4142-4 Includes bibliographical references (pages 173-174) and indexes.""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""Memoirs of the American Mathematical Society ;no. 905.Categories (Mathematics)Algebraic topologyCategories (Mathematics)Algebraic topology.512/.62Verity Dominic1966-1565967MiAaPQMiAaPQMiAaPQBOOK9910788852403321Complicial sets characterising the simplical nerves of strict -categories3836138UNINA