In detail, a morphism of pointed sets $f\colon \webleft (X,x_{0}\webright )\to \webleft (Y,y_{0}\webright )$ is a morphism of sets $f\colon X\to Y$ such that the diagram

commutes, i.e. such that

\[ f\webleft (x_{0}\webright ) = y_{0}. \]

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