  Presentations of smooth symmetry groups of differentiable stacks are studied
within the framework of the weak 2-category of Lie groupoids, smooth principal
bibundles, and smooth biequivariant maps. It is shown that principality of
bibundles is a categorical property which is sufficient and necessary for the
existence of products. Stacky Lie groups are defined as group objects in this
weak 2-category. Introducing a graphic notation, it is shown that for every
stacky Lie monoid there is a natural morphism, called the preinverse, which is
a Morita equivalence if and only if the monoid is a stacky Lie group. As
example we describe explicitly the stacky Lie group structure of the irrational
Kronecker foliation of the torus.
