Handbook of Model Categories

Scott Balchin currently holds a position at the Max Planck Institute for Mathematics, Germany. Previously he was a postdoctoral research fellow at the University of Warwick, England. He has published several articles on the use of Quillen model categories in various aspects of homotopy theory.

• Introduction.- Part I The theory and practice of model categories.- Introduction to Part I.- On Quillen model categories.- Properties.- New models from old.- Relation to (,1)-categories.- Part II Examples.- Introduction to Part II.- Simplicial sets.- Topological spaces.- Chain complexes.- Categories.- Spectra.- Simplicial categories.- Bisimplicial sets.- Relative categories.- Dendroidal sets.- Cyclic Sets.- C-algebras.- Miscellanea.- Part III A model categorical Kunstkammer.-Introduction to Part III.- Die Kunstkammer.- Bibliography.- Index.

“This book is a catalog of definitions, theorems, examples and counterexamples in model categories. … It is written both for beginners in this area of mathematics and for advanced researchers. In this book, the beginner will find an overview of the results in this area without being overwhelmed by technical details. The advanced researcher will be interested in having so many theorems and examples and counterexamples gathered in the same place.” (Philippe Gaucher, Mathematical Reviews, November, 2022)“This book is well-written and divided into eighteen chapters … . it can be said that this book will be one of the cult books about model categories in the literature, with its rich, diverse and current examples.” (Haydar Can Kaya, zbMATH 1486.18001, 2022)