Icons

Stephen Lack*

*Corresponding author for this work

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Categorical orthodoxy has it that collections of ordinary mathematical structures such as groups, rings, or spaces, form categories (such as the category of groups); collections of 1-dimensional categorical structures, such as categories, monoidal categories, or categories with finite limits, form 2-categories; and collections of 2-dimensional categorical structures, such as 2-categories or bicategories, form 3-categories.We describe a useful way in which to regard bicategories as objects of a 2-category. This is a bit surprising both for technical and for conceptual reasons. The 2-cells of this 2-category are the crucial new ingredient; they are the icons of the title. These can be thought of as "the oplax natural transformations whose components are identities", but we shall also give a more elementary description. We describe some properties of these icons, and give applications to monoidal categories, to 2-nerves of bicategories, to 2-dimensional Lawvere theories, and to bundles of bicategories.

Original languageEnglish
Pages (from-to)289-307
Number of pages19
JournalApplied Categorical Structures
Volume18
Issue number3
DOIs
Publication statusPublished - Jun 2010
Externally publishedYes

Keywords

  • 2-category
  • Bicategory
  • Icon
  • Oplax natural transformation
  • Pseudonatural transformation

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