 Density formula for presheaves (source code)

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= Density formula for presheaves
{title2=$X(U)\cong\int^W\mathcal C(U,W)\times X(W)$}

= Co-Yoneda lemma
{c}
{synonym}

For a <presheaf on a category>, the <categorical coend> identifies $(fh,x)$ with $(h,X(f)x)$. The displayed isomorphism sends the class of $(h:U\to W,x\in X(W))$ to $X(h)x$, with inverse $y\mapsto[1_U,y]$. The coend relation makes these inverse and natural. Consequently every presheaf is the <colimit> of representables indexed by its <category of elements>.

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