Higher Categories and Homotopical Algebra

Auteur

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).

Texte du rabat

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.

Résumé
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.

Contenu

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.