Differentiation of groupoid objects in tangent categories

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 Rosicky, which was later rediscovered by Cockett and Cruttwell. Mainly, I will construct the abstract Lie algebroid of a differentiable groupoid in a cartesian tangent category $C$ with a scalar $R$-multiplication, where $R$ is a ring object of $C$. Examples include differentiation of infinite-dimensional Lie groups, elastic diffeological groupoids, etc. This is joint work with Christian Blohmann.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)