3 papers
math.CT2026
Ehresmann connections in tangent categories
Geoffrey Cruttwell, Marcello Lanfranchi
The theory of connections is at the very core of differential geometry. Discovered by Levi-Civita and Christoffel and later studied by Cartan, Koszul, and others, connections appea…
math.CT2025
Pullbacks in tangent categories and tangent display maps
Geoffrey Cruttwell, Marcello Lanfranchi
In differential geometry, the existence of pullbacks is a delicate matter, since the category of smooth manifolds does not admit all of them. When pullbacks are required, often sub…
math.CT2024
A Tangent Category Perspective on Connections in Algebraic Geometry
G. S. H. Cruttwell, Jean-Simon Pacaud Lemay, Elias Vandenberg
There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical…