2-Dimensional Categories
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.
Cite
@article{arxiv.2002.06055,
title = {2-Dimensional Categories},
author = {Niles Johnson and Donald Yau},
journal= {arXiv preprint arXiv:2002.06055},
year = {2020}
}
Comments
Some typos fixed. The arxiv version will not be updated further. The authors hereby withdraw this book from the arxiv. A revised version will be published by Oxford University Press