A legal fight over allegations that a Minneapolis elected official tried to co-opt the name of a political critic’s blog ended quietly this week.

In a mediation conference Monday, blogger John Edwards and Carol Becker — an elected member of the Minneapolis Board of Estimate and Taxation — agreed to drop their respective lawsuits against one another. Edwards acknowledged that Becker did not threaten him personally or directly demand money from him. Becker agreed to give up her claim on the name “Wedge Live.”

The saga began this summer, when Becker applied for patents on “Wedge Live,” a moniker Edwards has used to blog and tweet political commentary for the past four years in south Minneapolis’ Wedge neighborhood. Becker said she planned to use it as the name of a national political podcast on wedge issues, and it had nothing to do with Edwards’ blog.

Edwards sued, alleging Becker was attempting to steal his brand to silence a critic. Becker sued him back.

On Friday, both parties claimed victory in the settlement.

“I did nothing to John Edwards,” said Becker. “What I did was legal, and when he asserted a claim I withdrew mine immediately. I think there was a whole bunch of smoke put out there that really wasn’t true.”

“I got what I needed,” said Edwards. “She tried to take Wedge Live from me, something that I clearly own and have spent four years building. ... She won’t come back and do it again, she agreed to that. So I’m glad we mounted a vigorous defense.”