4 papers
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…
Operads and Maurer-Cartan spaces
Daniel Robert-Nicoud
This thesis is divided into two parts. The first one is composed of recollections on operad theory, model categories, simplicial homotopy theory, rational homotopy theory, Maurer-C…
Convolution algebras and the deformation theory of infinity-morphisms
Daniel Robert-Nicoud, Felix Wierstra
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps…
A model structure for the Goldman-Millson theorem
Daniel Robert-Nicoud
By a result of Vallette, we put a sensible model structure on the category of conilpotent Lie coalgebras. This gives us a powerful tool to study the subcategory of Lie algebras obt…