Title: Two dimensional Lie theory

Abstract: This week I present an outline of a joint project with Ben MacAdam. The main aim is to generalise the theory of Lie groupoids and Lie algebroids by using 2-cubical sets. One advantage of this approach is that it avoids a certain quotient that is required in the classical theory and is therefore more amenable to generalisation in terms of tangent categories. An additional advantage of this approach is that when the tangent category is assumed representable the appropriate modification of the Lie approximation functor becomes representable also.