Morphisms of \$infty\$-groupoids

As far as I understand, there are several ways of defining $$infty$$-categories. One of them is to think of $$infty$$-cateogries as $$top$$-enriched categories. Hence we can think of $$infty$$-groupoids as generalizing topological groups. Functors between groupoids are the generalization of group homomorphisms. Hence my question is if $$infty$$-functors of $$infty$$-groupoids generalize continous group-homomorphisms? For instance, if $$G,H$$ are topological groups, and $$BG,BH$$ denote the associated topological groupoid/$$infty$$-groupoids, do we have
$$text{Hom}_{inftytext{-gpd}}(BG,BH)cong text{Hom}_{cont}(G,H)?$$