Higher Categories and Homotopical Algebra
Seiten
2019
Cambridge University Press (Verlag)
978-1-108-47320-0 (ISBN)
Cambridge University Press (Verlag)
978-1-108-47320-0 (ISBN)
This user-friendly book introduces modern homotopy theory through the lens of higher categories after Joyal and Lurie. Starting from scratch it guides graduate students and researchers through the powerful tools that the theory provides for applications in such areas as algebraic geometry, representation theory, algebra and logic.
This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch - revisiting results from classical homotopy theory such as Serre's long exact sequence, Quillen's theorems A and B, Grothendieck's smooth/proper base change formulas, and the construction of the Kan–Quillen model structure on simplicial sets - and develops an alternative to a significant part of Lurie's definitive reference Higher Topos Theory, with new constructions and proofs, in particular, the Yoneda Lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors. For graduate students and researchers from neighbouring fields, this book is a user-friendly guide to advanced tools that the theory provides for application.
This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch - revisiting results from classical homotopy theory such as Serre's long exact sequence, Quillen's theorems A and B, Grothendieck's smooth/proper base change formulas, and the construction of the Kan–Quillen model structure on simplicial sets - and develops an alternative to a significant part of Lurie's definitive reference Higher Topos Theory, with new constructions and proofs, in particular, the Yoneda Lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors. For graduate students and researchers from neighbouring fields, this book is a user-friendly guide to advanced tools that the theory provides for application.
Denis-Charles Cisinski is Professor of Mathematics at the Universität Regensburg, Germany. His research focuses on homotopical algebra, category theory, K-theory and the cohomology of schemes. He is also the author of a monograph entitled Les préfaisceaux comme modèles des types d'homotopie (2007).
Preface; 1. Prelude; 2. Basic homotopical algebra; 3. The homotopy theory of ∞-categories; 4. Presheaves: externally; 5. Presheaves: internally; 6. Adjoints, limits and Kan extensions; 7. Homotopical algebra; References; Notation; Index.
| Erscheinungsdatum | 04.05.2019 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 234 mm |
| Gewicht | 750 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-108-47320-2 / 1108473202 |
| ISBN-13 | 978-1-108-47320-0 / 9781108473200 |
| Zustand | Neuware |
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