2 citations · 4 across the 9 of their papers we have counts for
9 papers
From Abelianization to Tangent Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay, Tim Van der Linden
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of…
Tangent structures for divided power algebras
Sacha Ikonicoff
We build a tangent structure on the category of divided power algebras using a particular notion of semidirect product. We show that this tangent structure admits an adjoint tangen…
Quillen (co)homology of divided power algebras over an operad
Ioannis Dokas, Martin Frankland, Sacha Ikonicoff
Barr--Beck cohomology, put into the framework of model categories by Quillen, provides a cohomology theory for any algebraic structure, for example André--Quillen cohomology of com…
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…
Cartesian Differential Comonads and New Models of Cartesian Differential Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay
Cartesian differential categories come equipped with a differential combinator that formalizes the derivative from multi-variable differential calculus, and also provide the catego…
Divided power algebras and distributive laws
Sacha Ikonicoff
We study the divided power structures over a product of operads with distributive law. We give a systematic method to characterise the divided power algebras over such a product fr…
Unstable algebras over an operad II
Sacha Ikonicoff
We introduce a notion of unstable algebra over an operad in general characteristic. We show that the unstable algebra freely generated by an unstable module is itself a free algebr…
Unstable algebras over an operad
Sacha Ikonicoff
The aim of this article is to define and study a notion of unstable algebra over an operad that generalises the classical notion of unstable algebra over the Steenrod algebra. For…
Divided power algebras over an operad
Sacha Ikonicoff
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, followi…