Abstract
This book 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, adjunctions and
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.
Description
[2002.06055] 2-Dimensional Categories
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