We use the homotopy invariance of equivariant principal bundles to prove that the equivariant A-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds.
Keywords: Topological complexity, Lusternik-Schnirelmann category
2010 MSC: 55M30, 55R91
Theory and Applications of Categories, Vol. 35, 2020, No. 7, pp 179-195.