double category

Definitions Transfors between 2-categories Morphisms in 2-categories Structures in 2-categories Limits in 2-categories Structures on 2-categories A double category is an internal category in Cat. Similarly, a double groupoid is an internal groupoid in Grpd. However, these definitions obscure the essential symmetry of the concepts. We think of a double category as having We may picture a 2-cell in a double category as a square: Here are objects, and are horizontal arrows, and are vertical arrows.