Proof that the fundamental group is actually a group/Outline/Picture

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< Proof that the fundamental group is actually a group‎ | Outline
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[ilmath]\xymatrix{ \Omega(X,b)\times\Omega(X,b) \ar@2{->}[d]_{(\pi,\pi)} \ar[rr]^-{*} \ar@/^3.5ex/[drr]^(.75){\pi\circ *} & & \Omega(X,b) \ar[d]^{\pi} \\ \pi_1(X,b)\times\pi_1(X,b) \ar@{.>}[rr]_-{\overline{*} } & & \pi_1(X,b) }[/ilmath]
Factoring [ilmath]*[/ilmath] (loop concatenation) setup
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