Is the enriched $\underline{\mathrm{Top}}_{\mathrm{G}}$ tensored and cotensored?

Question

Let $\underline{\mathrm{Top}}_{\mathrm{G}}$ be the enriched category with objects topological spaces $X,Y...$ with $G$-action and morphisms all continuous maps $\mathrm{map}(X,Y)$ with the group $G$ acting by conjugation on the space $\mathrm{map}(X,Y).$ So this is a $\mathrm{Top}^G$-enriched category. See E. Riehl's "Categorical homotopy theory pp 39-41. Is it tensored and cotensored over $\mathrm{Top}^G$ ? Im guessing tensor should be the cartesian product with diagonal $G$-action and cotensor the function space with action by conjugation but im not so sure..