2007/02/19 by Stephen Lack · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:18C15 #msc:18C20 #msc:18D05 #msc:18G55 #msc:55U35
paper · pdf · doi:10.1007/978-1-4419-1524-5_4
73 pages; published in Towards Higher Categories, eds. John C. Baez and J. Peter May, Springer, 2009
arxiv created 2007/02/19 · openalex publication_date 2009/09/16 · arxiv updated 2010/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory, and nerves of bicategories. As is the way of these things, the choice of topics is somewhat personal. No attempt is made at either rigour or completeness. Nor is it completely introductory: you will not find a definition of bicategory; but then nor will you really need one to read it. In keeping with the philosophy of category theory, the morphisms between bicategories play more of a role than the bicategories themselves.