What is the meaning of the word "mate"?

Definitions:

a fellow member of a team noun
- It was my first start against my former teammates.
engage in sexual intercourse verb
- Birds mate in the Spring
one of a pair noun
- They lost the mate to their shoe.
place an opponent's king under an attack from which it cannot escape and thus ending the game verb
- The grandmaster checkmated their opponent after only a few moves.
the partner of an animal, especially a sexual partner noun
- The horse's mate was a thoroughbred champion.