Auk/Hyacinth/Chenille/Tartaros

Sorry, I wasn't clear enough. Of course he kidnapped her. The question is why think it was for sacrifice that he did so. I don't think Tartaros wanted him to kidnap anyone; the woman he had in mind, Chenille, was there willingly. But Auk, who is in a confused state, hearing 'A woman is vital,' and finding that Chenille has gone, grabs the only woman to hand, Hyacinth, who, unsurprisingly, is unwilling. As to the real reason - I think Tartaros, who is going to send Auk to start a new colony, wants him to bring a potential partner with whom he can have children. Later, when recruiting people for the expedition, Auk says every man must bring a woman and every woman a man. . So, if she was vital...

He says 'Go to the woman.. A woman is vital.' So, he has a particular woman in mind, but she matters because she is a a woman (not because she is a prostitute, or Silk's sister, or....) My explanation makes sense of this, I think.