The Phrygian cap

The Phrygian cap is a soft conical cap with the top pulled forward, associated in antiquity with several peoples in Eastern Europe and Anatolia, including Phrygia, Dacia and the Balkans.

In early modern Europe it came to signify freedom and the pursuit of liberty through a confusion with the pileus, the felt cap of manumitted (emancipated) slaves of ancient Rome. Accordingly, the Phrygian cap is sometimes called a liberty cap; in artistic representations it signifies freedom and the pursuit of liberty.

It is used in the coat of arms of certain Republics (like Haiti, Argentina, Cuba and Columbia) or of republican State institutions (like the US Senate) in the place where otherwise a Crown would be used (in the heraldry of monarchies). It thus came to be identified as a symbol of the republican form of government. A number of national personifications, in particular France's Marianne, are commonly depicted wearing the Phrygian cap.

Of course, its similarity with the Catalan barretina is no coincidence; it is a direct descendent of the Phrygian Cap.

https://southpacificberets.com/catalan-barretines.php