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Exercise $6 (b)$, page 58 from Hungenford's book Algebra.

Show that in $\mathcal{S}_{\star}$ (the category of pointed sets) every family of objects has a coproduct (often called a "wedge product"); describe this coproduct.

I need a suggestion in order to find the coproduct. I would appreciate your help.

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    No problem! Reposting as an answer.2012-02-23

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HINT: With two normal sets, the coproduct is the disjoint union. With pointed sets, you merely add the condition that the basepoints of both sets always go to the basepoint of the new set, which only requires a small modification to the disjoint union.

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    @magma: the coproduct of pointed sets $(X_i,b_i)$ is the universal pointed set $(X,b)$ with inclusion maps $f_i:(X_i,b_i)\to (X,b)$. By definition of morphisms between pointed sets, $f_i(b_i)=b$: all basepoints are mapped to the new basepoint.2012-02-25