1 citations · 1 across the 11 of their papers we have counts for
11 papers
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…
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…
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…
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…
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…
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 tangent…
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…
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…
The Grothendieck construction in the context of tangent categories
Marcello Lanfranchi
The Grothendieck construction establishes an equivalence between fibrations, a.k.a. fibred categories, and indexed categories, and is one of the fundamental results of category the…
The differential bundles of the geometric tangent category of an operad
Marcello Lanfranchi
Affine schemes can be understood as objects of the opposite of the category of commutative and unital algebras. Similarly, -affine schemes can be defined as objects of…
The Rosický Tangent Categories of Algebras over an Operad
Sacha Ikonicoff, Marcello Lanfranchi, Jean-Simon Pacaud Lemay
Tangent categories provide a categorical axiomatization of the tangent bundle. There are many interesting examples and applications of tangent categories in a variety of areas such…