Icons

Understand

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.