• Associativity. Given a diagram

    in $\mathsf{Sets}$, we have isomorphisms of sets

    \[ \webleft (A\times _{X}B\webright )\times _{Y}C\cong \webleft (A\times _{X}B\webright )\times _{B}\webleft (B\times _{Y}C\webright ) \cong A\times _{X}\webleft (B\times _{Y}C\webright ), \]

    where these pullbacks are built as in the diagrams


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