22 citations · 63 across the 24 of their papers we have counts for
8 papers · 1 filter
Moore-Penrose Dagger Categories
Robin Cockett, Jean-Simon Pacaud Lemay
The notion of a Moore-Penrose inverse (M-P inverse) was introduced by Moore in 1920 and rediscovered by Penrose in 1955. The M-P inverse of a complex matrix is a special type of in…
Cartesian Differential Kleisli Categories
Jean-Simon Pacaud Lemay
Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The…
Reverse Tangent Categories
Geoffrey Cruttwell, Jean-Simon Pacaud Lemay
Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differenti…
Hopf Monads on Biproducts
Masahito Hasegawa, Jean-Simon Pacaud Lemay
A Hopf monad, in the sense of Bruguières, Lack, and Virelizier, is a special kind of monad that can be defined for any monoidal category. In this note, we study Hopf monads in the…
Classical Distributive Restriction Categories
Robin Cockett, Jean-Simon Pacaud Lemay
In the category of sets and partial functions, , while the disjoint union is the usual categorical coproduct, the Cartesian product becomes a restri…
Graded Differential Categories and Graded Differential Linear Logic
Jean-Simon Pacaud Lemay, Jean-Baptiste Vienney
In Linear Logic (), the exponential modality brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly o…
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…
Differential Bundles in Commutative Algebra and Algebraic Geometry
G. S. H. Cruttwell, Jean-Simon Pacaud Lemay
In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative rin…