Item 4 (00D5) — The Clowder Project

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As a Weighted Limit. We have
\[ A\pitchfork X\cong \text{lim}^{\webleft [A\webright ]}\webleft (X\webright ), \]

where in the right hand side we write:
- $A$ for the functor $A\colon \text{pt}\to \mathsf{Sets}$ picking $A\in \text{Obj}\webleft (\mathsf{Sets}\webright )$;
- $X$ for the functor $X\colon \text{pt}\to \mathsf{Sets}_{*}$ picking $\webleft (X,x_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$.

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