Across the United States, in Tuesday’s off-year elections, women prevailed in many key races: in the Washington State Senate, where a special election flipped control of the chamber to the Democrats; in mayoral races in Seattle, Manchester, N.H., and Charlotte, N.C.; and in New Jersey, where the nation’s first black female Democratic lieutenant governor will soon be seated. Since President Trump’s election a year ago, women around the country have flooded political training programs, and many have declared candidacies.