On the tangent groupoid of a filtered manifold

We give an intrinsic (coordinate-free) construction of the tangent groupoid of a filtered manifold. This is an analogue of Connes' tangent groupoid which is pertinent for the analysis of certain subelliptic differential operators. It is a deformation of the pair groupoid to a bundle of nilpotent groups. We also describe the analogous construction in the context of the adiabatic groupoids of a filtered Lie groupoid.