2-Dimensional Categories

Erscheinungsjahr 2021
ISBN: 978-0-19-887137-8
Verlag: Oxford University Press(UK)

Buch, Englisch, 636 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 1109 g

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.

Autoren/Hrsg.

Johnson, Niles

Yau, Donald

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

- 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

Über Autor(innen)

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.