The notion of retrocell in a double category with companions is introduced and its basic properties established. Explicit descriptions in some of the usual double categories are given. Monads in a double category provide an important example where retrocells arise naturally. Cofunctors appear as a special case. The motivating example of vertically closed double categories is treated in some detail.
Keywords: Double category, companion, retrocell, cofunctor, closed bicategory
2020 MSC: 18D05, 18C15, 18D15
Theory and Applications of Categories, Vol. 40, 2024, No. 5, pp 130-179.
Published 2024-04-02.
TAC Home