What is the meaning of the word "mace"?

Definitions:

A brand name commonly used generically for tear gas and pepper spray, used for self-defense. NOUN
- For personal safety on her nightly walks she carries a can of mace in her purse, ready to use if needed.
A heavily ornamented staff that is carried as a symbol of authority in formal processions, especially in parliament or university settings. NOUN
- The university chancellor walked ahead, with the bearer holding the ceremonial mace leading the procession at graduation.
A spice made from the dried reddish covering of the nutmeg seed, typically used in powdered form and has a flavor that is similar to nutmeg but slightly more delicate and aromatic. NOUN
- She added a pinch of mace to the apple pie filling to enhance tis flavor with a subtle, warm spice.
A type of blunt weapon, a heavy head on the end of a handle used to strike opponents, commonly made of metal or wood and was used by cavalry and foot soldiers for close combat during medieval times; effective at inflicting damage through armor. NOUN
- During the medieval reenactment, of of the actors wielded a mace, demonstrating how knights fought in battles.