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I have 2 independent servers - one _A_ for user (auth, refresh, details, registration), the other one _B_ - for data.
if I want to access data on server _B_, I need to validate token first of all, that means that in my _B_ server endpoint I need to call a `check` method from _A_ server. Is it correct?

my server is written in Kotlin, using ktor

I would say this is a arch decision, and not kotlin specific... 

depends on technology that you are using for authentication/validation, for example if you are using JWT you have all information to validate user without call check... assuming you don't care about revoke..
if you are using a different technology you probably need to call server B, depends... 