Oberseminar Deformationsquantisierung und Geometrie: Lory Aintablian (MPI Bonn)

Abstract: The infinitesimal counterpart of a Lie group(oid) is its Lie algebra(oid). I will show that the differentiation procedure works in any category with an abstract tangent structure in the sense of Rosick{\'y}. Mainly, I will construct the abstract Lie algebroid of a differentiable groupoid in a cartesian tangent category $\mathcal{C}$ with a scalar $R$-multiplication, where $R \in \mathcal{C}$ is a ring object. Examples include differentiation of infinite-dimensional Lie groups, elastic diffeological groupoids, etc. This is joint work with Christian Blohmann.