"the tea salon to the rooftop's hat factory"; meaning of "to"?

Question

During Prohibition, the Colony Arcade Building was part hat factory, part tea salon. Today, as the Refinery Hotel, it’s just as charmingly weird, and home to two bars. The Refinery Rooftop—accessible by elevator, with rigmarole—has a stunningly gorgeous view of the Empire State Building. There’s a retractable glass ceiling, a fireplace, high tables and low couches, tiered plates of food, and a menu of Bites, Dips, Flats, Crispies, and Balls. One evening, hotel guests posed for pictures holding flutes of champagne, and noisy young professionals drank sauvignon blanc. “It feels like a wedding venue in Chicago,” a woman said. Downstairs, hidden behind velvet curtains, is Winnie’s Lobby Bar, the tea salon to the rooftop’s hat factory.

What does to mean in the bolded section?

Answer 1

This is an analogy suggesting that the relationship between Winnie's Lobby Bar and The Refinery Rooftop is similar in some way to that between the tea salon and the hat factory which once occupied that building. This follows a common form for analogies which is structured as follows:

A is the X to B's Y

In this form there is a known relationship between X and Y, and the intent is to communicate the same or similar relationship between A and B.

This is a common way to express an analogy using familiar concepts. For example, if you wanted to express to a close friend that they keep you balanced, and you feel you do the same for them, you might make an analogy to the concept of Yin and Yang (found in Chinese and Taoist philosophy) using the same structure:

You are the Yin to my Yang

Another common format you may see for analogies is a bit more verbose. It still conveys the same similarity between two relationships. This format takes the following form:

A is to B as X is to Y

This format sounds a bit more academic and less literary than the earlier one, and is often the preferred format seen on some standardized tests, such as previous formats of the SAT.

_{Hope that helps.}

Answer 2

It's short for "in analogy to". That is, as the tea salon related to the hat factory, so Winnie's relates to the Rooftop.