I suspect what you're referring to is a Top Hat. The tall black hats that gentlemen wear to formal occasions.
if you have an opera hat case
If by 'opera hat' you mean a top hat, it might be collapsible, which would make it easy to pack. Read more, below.
I would call it a hard hat
musical, opera maybe?
A Place to Call Home - opera - was created in 1993.
The Bowler and the Derby is the same hat. The British call the hat a Bowler. The Americans call the hat a Derby.
Flat hat
In opera, the text is written by a librettist.
The libretto.
A Panama hat.
The hat is also called a homburg hat in English.
rizal wears a bowler hat.