2024/09/14 by Paré, Robert
#12H10 #18A22 #18D60 #18F20 #18F40 (Primary) 18F50 (Secondary) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.09494
Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \citePar24 to the multivariable case. These combine into the Jacobian profunctor which provides the setting for a lax chain rule. We introduce a functorial version of multivariable Newton series whose aim is to recover a functor from its iterated differences. Not all functors are recovered but we get a best approximation in the form of a left adjoint, and the induced comonad is idempotent. Its fixed points are what we call soft analytic functors, a generalization of the multivariable analytic functors of Fiore et al.~\citeFioGamHylWin08.