000			01628 a2200217 4500
999			_c54443 _d54443
008			210324b ||||| |||| 00| 0 eng d
020			_a9781108479622
082			_a514.24 _bRIC
100			_aRichter, Birgit
245			_aCategories to homotopy theory
260			_bCambridge University Press, _c2020. _aCambridge:
300			_ax, 390 p. : _bhb, _c24 cm.
365			_aGBP _b49.99
440			_aCambridge studies in advanced mathematics ; 188.
520			_aCategory theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
650			_aCategories (Mathematics)
650			_aHomotopy theory
650			_aTopology
650			_aMathematics
942			_2ddc _cTD