2-Dimensional Categories

Understand

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.