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
$$text{Hom}_{inftytext{-gpd}}(BG,BH)cong text{Hom}_{cont}(G,H)?$$