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math.CT2023
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…
math.AG2023
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…
math.CT2023★ 1 cited
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…