Template:Double category/doc

Usage

 * Think of a double category as having any of several fundamental and distinct classes to which entities or concepts belong articles that fall into one of several categories. 2 : a division within a system of classification as in a category, or a a written composition in prose, usually nonfiction, on a specific topic, forming an independent part of a book or other publication, as a newspaper or magazine. an individual object, member, or portion of a class, as in a article.
 * Any 2-category can also be made into a double category in two more ways, by defining the vertical or horizontal morphisms to consist only of identities. In this way 2-categories can be considered as a special case of double categories.
 * There are notions of functor and of transformation between double categories, which make them into a 2-category. In fact, due to the vertical-horizontal symmetry, there are two such 2-categories, depending on the direction we choose the transformations to go in. Moreover, we can also take the functors to be strict, pseudo, lax, or colax in either direction, so there are many possible 2-categories of double categories (although for some choices one has to worry about compatibility).