I was reading this wiki article on a recent lengthy trip down the wikipedia rabbit-hole: https://en.wikipedia.org/wiki/Giovanni_da_Pian_del_Carpine

In 1245 Giovanni (or Johannes on wiki) was sent by Pope Innocent IV as the first formal Catholic mission to the Mongols. He eventually made it all the way to Mongolia and the court of Güyük Khan, who had just been enthroned. Amongst other thing, Johannes asked the Khan to convert to Christianity (he said no). Wiki then says:

He [Guyuk Khan] gave them a letter to the Pope—written in Mongol, Arabic, and Latin—that was a brief imperious assertion of the Khan's office as the scourge of God.

My fundamental question is: How were they able to compose it in Latin? AFAIK, the Mongols only even reached the eastern edges of Europe in 1237. So, did the Mongols have their own Europeans kept at court for this purpose? Did they communicate in Arabic as a middle ground language that some Europeans and some Mongols would both know?

I'd also be interested in the reverse of this question, i.e.: Would Pope Innocent IV have had people available to him who spoke Mongol?

Again from wiki: Johannes took with him Benedict of Poland who acted as his 'translator' - (https://en.wikipedia.org/wiki/Benedict_of_Poland). What languages he was translating from/to is not clear as wiki only says he spoke Latin.

More generally, I'm surprised this story of an official European Catholic mission hanging out in the Mongol capital for a while isn't better known. Especially given the ongoing fascination with Marco Polo who maybe didn't do anything in the Far East, and if he did, did it much later anyway.