if the gitlab first, I want the other app use gitlab cookie to login

Problem to solve

I am using gitlab as oauth IDP. now I want to do a new feature:

1. the user login gitlab first
2. the user open other application in the same browser.
3. the other application can use the gitlab's cookie or session or token to login

Proposal

so I want to know:

1. which gitlab cookie I can use ?
2. is there a api to validate the cookie and which user is using this cookie ?