We develop further the theory of monoidal bicategories by introducing and studying bicate- gorical 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.

翻译：我们通过引入并研究线性逻辑研究中考虑的线性指数余单模范畴的对偶概念，以及微分范畴中为研究微分线性逻辑而引入的余对偶变换的范畴论对应，进一步发展了幺半双范畴理论。作为应用，我们将Joyal解析函子的微分演算推广到预层范畴间的解析函子，正如普通微积分从单变量推广到多变量情形。