The Homotopy Theory of (∞,1)-Categories (London Mathematical

The Homotopy Theory of (∞,1)-Categories (London Mathematical Society Student Texts, Series Number 90)

The notion of an (âˆž,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.
Country USA
Brand Cambridge University Press
Manufacturer Cambridge University Press
Binding Paperback
ReleaseDate 2018-03-15
UnitCount 1
EANs 9781107499027

The Homotopy Theory of (∞,1)-Categories (London Mathematical Society Student Texts, Series Number 90)