Exactly -- the diaeresis separates the two letters so that each makes their own sound.
It's sometimes used in English as well, e.g. in naïve to show that it's not pronounced like "knave" but rather like "na-eeve", or in old-fashioned spelling in coöperate to show that the first part does not sound like "cooper".
You are definitely the best commenter i've seen on duolingo. Thanks for another great explanation!
I thought that was how Greek people said ‘you’re not the boss of me’... Apparently it’s an Archer reference.
είσαι is the verb form for "you".
She/He would require the verb form είναι. (With nu in the middle rather than sigma.)
The two dots are a dieresis -- they serve to show that the vowel is pronounced separately.
For example, the English word naïve has two syllables na-ïve and doesn't rhyme with waive (one's rights).
Similarly here, προϊστάμενος has five syllables προ-ϊσ-τά-με-νος, rather than having οι pronounced as one vowel sound /i/.