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math.CT2026
The Lie group-Lie algebra correspondence in tangent categories
Marcello Lanfranchi
Classic Lie theory establishes a correspondence between Lie groups, which are internal group objects in the category of smooth manifolds, and Lie algebras. An analogous corresponde…
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.CT2026
The formal theory of tangentads PART II
Marcello Lanfranchi
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functo…