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.

翻译：我们进一步发展了幺半双范畴的理论，通过引入并研究线性逻辑中考虑的线性指数余单子概念的双范畴对应物，以及为通过微分范畴研究微分线性逻辑而引入的余导数变换的双范畴对应物。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一样。