TITLE: What is an example of a colimit-dense generator which is not dense?
QUESTION [5 upvotes]: 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?

REPLY [9 votes]: $\Bbb R$ 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").