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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…