The condition that $C \to \mathrm{Set}^{C^{op}} \to \mathrm{Set}^{B^{op}}$ is fully faithful is obviously equivalent to the condition that for every $c \in C$ the set of *all* morphisms from objects in $B$ to $c$ is a colimit diagram. In other words, $c$ is the colimit of the canonical diagram $(B \downarrow c) \to B \to C$. Therefore one then calls $B$ a **dense** subcategory of $C$. If you just require that every $c$ is *some* colimit of a diagram which factors over $B$, then $B$ is called **colimit-dense**. This is a weaker condition: $\{R\}$ is not dense in $\mathrm{Mod}(R)$, but it is colimit dense. Note that already $\{R \oplus R\}$ is dense in $\mathrm{Mod}(R)$.

You can find more about dense subcategories at the [nlab][1] and in Exercise 12.D of "Abstract and Concrete Categories - The Joy of Cats" ([online][2]). The definition also plays a central role in the definition of locally presentable categories; see the book by Adamek and Rosicky.


  [1]: http://ncatlab.org/nlab/show/dense+subcategory
  [2]: http://katmat.math.uni-bremen.de/acc/acc.pdf