A profinite group is said to be projective if its cohomological dimension is $\leq 1$. Is this related to some other notion of "projective"? How so?



What's "projective" about "projective pro-finite groups"?
A profinite group $P$ is projective if and only if any continuous group homomorphism from it to a profinite quotient group $G/H$ lifts to a continuous group homomorphism to the profinite group $G$.


