Morita equivalence for $L_\infty$-groupoids

Abstract: $L_\infty$-groupoids provide ``charts'' for higher differentiable stacks. Morita equivalent ones should present the same stack. In a joint work with Christian Blohmann, inspired by Lurie's correspondence between simplicial sets, we construct all higher bibundles between $L_\infty$-groupoids and define what principality means via Kan conditions. Thus, as a bi-principal bibundle provides Morita equivalence between Lie groupoids, we naturally extend Morita equivalence to higher Lie groupoids. We then show this version of Morita equivalence does correspond to isomorphisms between stacks, thus fulfills its functionality. In this talk, we will give an introduction to the theory of higher Lie groupoids, and their Morita equivalence in the form of bibundles.