214 citations · 588 across the 26 of their papers we have counts for
8 papers · 1 filter
Simplicial properadic homotopy
Eric Hoffbeck, Johan Leray, Bruno Vallette
In this paper, we settle the homotopy properties of the infinity-morphisms of homotopy (bial)-gebras over properads, i.e. algebraic structures made up of operations with several in…
Higher Lie theory
Daniel Robert-Nicoud, Bruno Vallette
We present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers…
The diagonal of the associahedra
Naruki Masuda, Hugh Thomas, Andy Tonks +1
This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplice…
Symmetric homotopy theory for operads
Malte Dehling, Bruno Vallette
The purpose of this foundational paper is to introduce various notions and constructions in order to develop the homotopy theory for differential graded operads over any ring. The…
Homotopy theory of homotopy algebras
Bruno Vallette
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more…
Algebra+Homotopy=Operad
Bruno Vallette
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the n…