3 papers
math.CT2019
Involution algebroids: a generalisation of Lie algebroids for tangent categories
Matthew Burke, Benjamin MacAdam
We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in…
math.CT2017
The Algebroid of a Groupoid in a Tangent Category
Matthew Burke
We generalise the construction of the Lie algebroid of a Lie groupoid so that it can be carried out in any tangent category. First we reconstruct the bijection between left invaria…
math.CT2016
A Synthetic Version of Lie's Second Theorem
Matthew Burke
We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we gene…