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2-Dimensional Categories

Auteur Niles Johnson
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2-Dimensional Categories
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2-Dimensional Categories
2-Dimensional Categories
Als nieuw
32,50
10000130627
ISBN
9780198871385
Bindwijze
Paperback
Taal
Engels
Auteur
Niles Johnson
Uitgeverij
Oxford University Press
Jaar van uitgifte
2021
Aantal pagina's
640

Waar gaat het over?

2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. 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.
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