5 papers
Localisation of cubical model categories
Brice Le Grignou
In this article we introduce the notion of a square structure on a model category, that generalises cubical model categories. We then show that under some homotopical conditions on…
Presentations of algebras in chain complexes
Brice Le Grignou
The goal of this article is to describe several presentations of the infinity category of algebras over some monad on the infinity category of chain complexes.
Base change along lax squares
Brice Le Grignou, Damien Lejay
In this note we present a recipe which transforms any pull-push along a span of categories into a push-pull along a cospan and vice versa, based on a theorem from Guitart.
Operads without coalgebras
Brice Le Grignou, Damien Lejay
We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.
Cubical model categories and quasi-categories
Brice Le Grignou
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cu…