From categories to homotopy theory:
Category 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 acc...
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| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2020
|
| Series: | Cambridge studies in advanced mathematics
188 |
| Links: | https://doi.org/10.1017/9781108855891 |
| Summary: | Category 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. |
| Physical Description: | 1 Online-Ressource (x, 390 Seiten) |
| ISBN: | 9781108855891 |
Staff View
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| spelling | Richter, Birgit 1971- From categories to homotopy theory Birgit Richter Cambridge Cambridge University Press 2020 1 Online-Ressource (x, 390 Seiten) txt c cr Cambridge studies in advanced mathematics 188 Category 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. Erscheint auch als Druck-Ausgabe 9781108479622 |
| spellingShingle | Richter, Birgit 1971- From categories to homotopy theory |
| title | From categories to homotopy theory |
| title_auth | From categories to homotopy theory |
| title_exact_search | From categories to homotopy theory |
| title_full | From categories to homotopy theory Birgit Richter |
| title_fullStr | From categories to homotopy theory Birgit Richter |
| title_full_unstemmed | From categories to homotopy theory Birgit Richter |
| title_short | From categories to homotopy theory |
| title_sort | from categories to homotopy theory |
| work_keys_str_mv | AT richterbirgit fromcategoriestohomotopytheory |