the capi
The cap that was worn by the common soldiers during the American Revolution was called a tricorn. The shako cap can be traced back to War of 1812.
Kepi
A woolen cap worn in Scotland is called a tam o' shanter.
The skull cap worn by a pope, cardinal or bishop is called a zucchetto.
The 'cap' (beanie) worn by some priests, and all bishops, cardinals and the pope is called a zucchetto.
A square clerical cap is called a biretta. This traditional headgear is commonly worn by clergy members, particularly in the Catholic Church, to signify their rank or office.
The caps are called zucchetto. Zucchetto: noun: a small round skullcap worn by members of the Roman Catholic clergy, the color of which depends on the rank of the person wearing it
These are normally called Mercury dimes because the winged cap worn by Miss Liberty looks a lot like the cap worn by the god Mercury. See the related link for values
A bathing cap is a silicone, latex or lycra cap which is worn on the head by swimmers.
A priests skull cap is called a "Zuchetto". Another name for it is a "Callote". Ref: www.myfreedictionary.com
The graduation "cap" is called a mortar I believe. The cap and tassel have a long history of educational significance. The graduation cap today continues to signify personal and academic achievement, despite the fact it's only worn for a few hours!
The cap worn by matador is called a montera. The American bullfighter wears a traditional cowboy hat.