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2-Dimensional Categories - Oxford Scholarship Online
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2-Dimensional Categories

Niles Johnson and Donald Yau

Abstract

2-Dimensional Categories provides 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; the 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 ... More

Keywords: 2-category, bicategory, pasting diagram, lax functor, bilimit, 2-monad, Bicategorical Yoneda Lemma, coherence, Grothendieck construction, monoidal bicategory

Bibliographic Information

Print publication date: 2021 Print ISBN-13: 9780198871378
Published to Oxford Scholarship Online: February 2021 DOI:10.1093/oso/9780198871378.001.0001

Authors

Affiliations are at time of print publication.

Niles Johnson, author
Associate Professor of Mathematics, Ohio State University

Donald Yau, author
Professor of Mathematics, Ohio State University