2 citations · 4 across the 7 of their papers we have counts for
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Tangent -categories and Goodwillie calculus
Kristine Bauer, Matthew Burke, Michael Ching
We make precise the analogy between Goodwillie's calculus of functors in homotopy theory and the differential calculus of smooth manifolds by introducing a higher-categorical frame…
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…
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…
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry
Matthew Burke
We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids interna…
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…