3 papers
math.CT2020
Vector bundles and differential bundles in the category of smooth manifolds
Benjamin MacAdam
A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical diffe…
cs.LO2019
Reverse derivative categories
Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher +4
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivativ…
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…