Hom${}_{\ast }$ commuting with filtered products

In a sufficiently rich category, such as a category of R-modules, and a given infinite cardinal $\kappa$, we examine classes $\text{Cal}{H}_{\ast }^{\kappa }$ of objects M, such that the following natural monomorphism is an isomorphism: \prod_{i\in I}}^{\kappa}\hbox{\rm Hom}\,(M, A_i)\cong \hbox{\rm Hom}\,(M, \prod_{i\in I}}^{\kappa} A_i), for every family of objects $\{A_i,i\in I\}$ (${\prod }^{\kappa }$ denotes the subproduct of all the vectors with support $<\kappa$).