The Costume Institute is housed within the Metropolitan Museum of Art but exists in a separate universe, one with its own galleries, budget, press representative and aesthetic protocols. To some this fashion-world apart is a Martian oddity, to others it is a vital preserve of Venusian luxe. Either way — and for better and worse — it has never been as fully integrated with the Met as it is in the exhibition that opened this week called “China: Through the Looking Glass.”

Designed to illustrate the influence of Chinese culture on Western fashion, the show is spread over three floors.