2 citations · 4 across the 10 of their papers we have counts for
10 papers
Mapping coalgebras II: Operads
Brice Le Grignou
In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.
An homotopical description of small presheaves
Brice Le Grignou
This article describes the cocompletion of a category with finite limits as the homotopy category of some equivalence 2-groupoids in coproducts of elements of . This yields…
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…
Homotopy Theory of linear coalgebras
Brice Le Grignou, Damien Lejay
We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example $\ma…
Algebraic operads up to homotopy
Brice Le Grignou
This paper deals with the homotopy theory of differential graded operads. We endow the Koszul dual category of curved conilpotent cooperads, where the notion of quasi-isomorphism b…
From homotopy operads to infinity-operads
Brice Le Grignou
The goal of the present paper is to compare, in a precise way, two notions of operads up to homotopy which appear in the literature. Namely, we construct a functor from the categor…