connection on a double category
Let be a double category. A connection on is given by a pair of functions , that assign to each vertical morphism cells of the form
(where is the horizontal identity on ) such that and behave suitably with respect to composition and identities in :
(that is, they are identity-on-objects functors) and such that the vertical composite and the horizontal composite , (that is, and are companions).
Created on April 18, 2011 19:03:28
by Finn Lawler