If $\mathbf{C}$ is a category, then the Yoneda functor which sends $a$ to $Hom_\mathbf{C}(-,a)$ is a fully faithful embedding of categories $$ \mathbf{C}\rightarrow \mathbf{Func}( …

Let $\mathcal{A}$ be a small category with some ( maybe no) colimits. What I would like to be able to do is add the rest of the colimits in a universal way. The Yoneda lemma will n …

If we consider metric spaces to be categories enriched over $\mathbb R_{\geq 0}$, the object corresponding to presheaves should be lipschitz-continuous functions $\operatorname{Lip …