Induced monoidal structure from the functor

Let $mathcal{B}$ be a subcategory of a given category $mathcal{D}$. Let $mathcal{B}$ has monoidal structure. In this article, we discuss when can one extend the monoidal structure of $mathcal{B}$ to $mathcal{D}$ such that $mathcal{B}$ becomes a sub monoidal category of monoidal category $mathcal{D}$. Examples are discussed, and in particular, in an example of loop space, we elaborated all results discussed in this article.