2-Dimensional Categories

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Niles Johnson (Associate Professor of Mathematics, Associate Professor of Mathematics, Ohio State University) Donald Yau (Professor of Mathematics, Professor of Mathematics, Ohio State University)

2-Dimensional Categories

Niles Johnson (Associate Professor of Mathematics, Associate Professor of Mathematics, Ohio State University), Donald Yau (Professor of Mathematics, Professor of Mathematics, Ohio State University)

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English

Oxford University Press
14 February 2021

Mathematics & Sciences; Mathematics; Applied mathematics; Mathematical physics; Computer science

Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac Lane. It describes relationships between mathematical structures. Outside of pure mathematics, category theory is an important tool in physics, computer science, linguistics, and a quickly-growing list of other sciences. This book is about 2-dimensional categories, which add an extra dimension of richness and complexity to category theory. 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.

By: Niles Johnson (Associate Professor of Mathematics Associate Professor of Mathematics Ohio State University), Donald Yau (Professor of Mathematics, Professor of Mathematics, Ohio State University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 31mm, Width: 157mm, Spine: 234mm
Weight: 105g
ISBN: 9780198871385
ISBN 10: 0198871384
Pages: 640
Publication Date: 14 February 2021
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

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

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.