2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165807Presentations 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.40 pages; definition of group objects in higher categories added; coherence relations for groups in 2-categories given (section 4)Differential GeometryHigh Energy Physics - TheoryCategory Theory20N99; 18B40, 58A03, 58H05text