= Covariant density presentation
{title2=$F\cong\operatorname{colim}_{(c,x)\in(\int F)^{\mathrm{op}}}\mathcal C(c,-)$}
For a set-valued covariant <functor> on a <small category>, the <Yoneda lemma> sends the element $x\in F(c)$ to the transformation $\mathcal C(c,-)\to F$. These transformations form a <cocone> indexed by the opposite <category of elements>. At $a$, send the representative $(c,x,u:c\to a)$ to $F(u)x$. It is surjective using $(a,z,1_a)$; two representatives of $z$ are identified through that same object of the <category of elements>. This proves the displayed presentation pointwise.
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