8 papers
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…
Local categories: a new framework for partiality
Marcello Lanfranchi, Jean-Simon Pacaud Lemay
Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categori…
Representable tangent structures for affine schemes
Marcello Lanfranchi, Jean-Simon Pacaud Lemay
The category of affine schemes is a tangent category whose tangent bundle functor is induced by Kähler differentials, providing a direct link between algebraic geometry and tangen…
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…
The formal theory of tangentads PART I
Marcello Lanfranchi
Tangent categories offer a categorical context for differential geometry, by categorifying geometric notions like the tangent bundle functor, vector fields, Euclidean spaces, vecto…
Tangentads: a formal approach to tangent categories
Marcello Lanfranchi
Tangent category theory is a well-established categorical context for differential geometry. In a previous paper, a formal approach was adopted to provide a genuine Grothendieck co…