A certificate is not cryptography, though, it's a number. The entity requesting the certificate already has the cryptographic software installed on their server

A certificate is not cryptography, though, it's a number. The entity requesting the certificate already has the cryptographic software installed on their servers, as do the clients trying to connect to them. There's nothing technologically special about the number, it's all in the realm of the social contract, in that it has been blessed by a chain of trust.