authority, yes

διὰ τοῦτο ὀφείλει ἡ γυνὴ ἐξουσίαν ἔχειν ἐπὶ τῆς κεφαλῆς διὰ τοὺς ἀγγέλους is a wonderful verse when you take it literally. It makes one wonder about our culture as opposed to the early churches practice of allowing women to minister, prophesy and pray in public. Google's funny tranlation is "Therefor due or woman possessing the power to become on their heads on account of the angels". I found this definition of "angels". “Messengers of the Congregation”, mentioned in Jewish sources, worship-leaders similar to today’s הון?