The box-like caps are called biretta ( singular birettum)
Bishops wear purple ones.
Cardinals wear red.
There is a red brimmed hat the cardinals may wear called a galero.
The skullcap worn by bishops, cardinals and the pope is called a zucchetto.
The bishop's ceremonial hat is called a mitre.
The bishop's ceremonial hat is called a mitre.
it is called a mitre
I don't think the Holy Father's hat's point has a name. The "hat" you usually see him in is a miter (or mitre, it is spelled both ways), all bishops wear one when vested (in liturgical vestments).
The red hat club
The Galero.
A building witha broken pitch (bonnet) roof, also called witches cap, and in france its called a pepper pot, or bishops mitre.
Mitre
Initially it was just called "Red Hat Linux", but now Red Hat focuses exclusively on the enterprise market with its Linux distribution named "Red Hat Enterprise Linux" (RHEL) with the community version named CentOS (Community ENTerprise Operating System) and Fedora (a Red Hat-supported community Linux distribution)
The valve that resembles a bishop's hat is called the "mitral valve." Named for the mitre worn by bishops, this valve is located between the left atrium and left ventricle of the heart. It plays a crucial role in ensuring that blood flows in one direction, preventing backflow as the heart pumps.
The Golden Hat
Raho-tu (Mitre Peak), Milford Sound, Fiordland, South Island, NZ.