2-Dimensional Categories
Oxford University Press (Verlag)
978-0-19-887138-5 (ISBN)
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2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax functors, 2-/bilimits, the Duskin nerve, 2-nerve, internal adjunctions, monads in bicategories, 2-monads, biequivalences, the Bicategorical Yoneda Lemma, and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.
Niles Johnson is an Associate Professor of Mathematics at The Ohio State University at Newark. He obtained his PhD at University of Chicago and held a post-doctoral position at the University of Georgia. His research focuses on algebraic topology. Donald Yau is a Professor of Mathematics at The Ohio State University at Newark. He obtained his PhD at MIT and held a post-doctoral position at the University of Illinois at Urbana-Champaign. His research focuses on algebraic topology. He has published 7 books and over 40 research articles.
1: Categories
2: 2-Categories and Bicategories
3: Pasting Diagrams
4: Functors, Transformations, and Modifications
5: Bicategorical Limits and Nerves
6: Adjunctions and Monads
7: The Whitehead Theorem for Bicategories
8: The Yoneda Lemma and Coherence
9: Grothendieck Fibrations
10: The Grothendieck Construction
11: The Tricategory of Bicategories
12: Further 2-Dimensional Categorical Structures
Erscheinungsdatum | 13.02.2021 |
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Verlagsort | Oxford |
Sprache | englisch |
Maße | 157 x 31 mm |
Gewicht | 105 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Naturwissenschaften ► Physik / Astronomie | |
ISBN-10 | 0-19-887138-4 / 0198871384 |
ISBN-13 | 978-0-19-887138-5 / 9780198871385 |
Zustand | Neuware |
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