Title: Exponential Functions for Cartesian Differential Categories. Abstract: We introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function from classical differential calculus. In particular, differential exponential maps can be defined without the need for limits, converging power series, multiplication, or unique solutions of certain differential equations -- which most Cartesian differential […]

# Event categories Archives:

## Michael Ching

Title: Day convolution, infinity-operads and Goodwillie calculus (slides) Abstract: Goodwillie calculus is a branch of homotopy theory that provides systematic approximations to a suitable functor (say from the category of topological spaces to itself) in the form of a "Taylor tower", analogous to the Taylor series from ordinary calculus. In this talk, I will describe […]

## Sarah Yeakel

Title: Operads with homological stability Abstract: For a carefully constructed operad M of surfaces, Tillmann showed that algebras over M group complete to infinite loop spaces. This result relies, in part, on Harer's homological stability theorem for mapping class groups of surfaces. We will review Tillmann's result and provide a more general framework which shows […]

## Rick Blute

Title: Ribenboim's generalized power series and weighted Rota-Baxter categories (slides)

## JS Lemay

Title: Lifting Coalgebra Modalities Abstract: In this talk we will look at lifting coalgebra modalities (both monoidal and non-monoidal) to Eilenberg-Moore categories of suitable monads. In particular we introduced mixed distributive laws of monads over coalgebra modalities. We will also see how every monoid in the co-Eilenberg-Moore category of a monoidal coalgebra modality induces these […]

## Geoff Cruttwell

Title: Affine spaces in a tangent category. Abstract: Affine manifolds are smooth manifolds with a particular choice of charts such that each transition function is affine. In addition to being interesting in their own right, recent work of Jubin showed that the category of affine manifolds has a wide variety of monads and comonads on […]

## Brenda Johnson

Title: Functor calculus and precalculus Abstract: Functor calculi have been developed in a variety of forms and contexts for use in algebraic topology and homological algebra. Examples include the manifold calculus of Tom Goodwillie and Michael Weiss, Goodwillie's calculus of homotopy functors, Weiss' orthogonal calculus, and the discrete calculi for abelian and simplicial model categories […]