Algebra all Products Mathematics

2-Dimensional Categories

Johnson, Niles

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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.

Accessories:

No Accessory

Publisher

OXFORD UNIV PR

Bisac Major Subject

Mathematics

Binding Type

Paperback

Country Of Origin

Number Of Units

Length

9.1 Inches

Barcode Indicator

EAN

Width

6.1 Inches

Publication Date

1970-01-01

Height

1.4 Inches

ISBN 10

0198871384

Weight

2.35 Pounds

Book EAN

9780198871385

Target Audiance

Adults

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2-Dimensional Categories