An object $G$ of a category $\mathcal{C}$ is a *dense generator* if every object $X$ is the colimit of the canonical diagram of copies of $G$ mapping to $X$. (This canonical diagram is indexed by the full subcategory of the slice $\mathcal{C}\_{/X}$ on the objects of the form $G \to X$.)


An object $G$ is called a *colimit-dense generator* if every object $X$ is a colimit of *some* diagram of copies of $G$. (That means $X$ is the colimit of some functor $F : \mathcal{I} \to \mathcal{C}$ with $F(i) = G$ for all objects $i$.)


Is there an example of a colimit-dense generator which is not a dense generator?



What is an example of a colimit-dense generator which is not dense?
$\Bbb R$ is colimit-dense in the category of real vector spaces but not dense
(see 6.F, 6.34 in my book with J. Adámek ["Locally presentable and accessible categories"](http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511600579)).


