  We develop further the theory of monoidal bicategories by introducing and
studying bicategorical counterparts of the notions of a linear explonential
comonad, as considered in the study of linear logic, and of a codereliction
transformation, introduced to study differential linear logic via differential
categories. As an application, we extend the differential calculus of Joyal's
analytic functors to analytic functors between presheaf categories, just as
ordinary calculus extends from a single variable to many variables.
