Shifted Contact Structures on Differentiable Stacks

We define 0-shifted and +1-shifted contact structures on differentiable stacks, thus laying the foundations of shifted Contact Geometry. As a side result we show that the kernel of a multiplicative 1-form on a Lie groupoid (might not exist as a Lie groupoid but it) always exists as a differentiable stack, and it is naturally equipped with a stacky version of the curvature of a distribution. Contact structures on orbifolds provide examples of 0-shifted contact structures, while prequantum bundles over +1-shifted symplectic groupoids provide examples of +1-shifted contact structures. Our shifted contact structures are related to shifted symplectic structures via a Symplectic-to-Contact Dictionary.