This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume.
The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.

Highlights the key points of the theory before discussing various properties and structures that a model category may have Boasts over 200 pages of examples of model categories in algebra and topology, and everything in between, ranging over 12 themes Features a table of curiosities highlighting a range of, sometimes unexpected, phenomena that occur when working with model categories

Autorentext

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.

Inhalt
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.