In this talk we introduce some natural constructions from the "graded world": graded Hopf algebras and differential graded Harish-Chandra pairs. We also discuss some properties of functional spaces on graded manifolds. These constructions are then used to solve the integration problem of differential graded Lie algebras to differential graded Lie groups.
This is a joint work with Alexei Kotov, based on  and its extensions.
 B. Jubin, A. Kotov, N. Poncin, V. Salnikov, Differential graded Lie groups and their differential graded Lie algebras, to appear in Transformation Groups, 2021.