Ory is the largest open source community in the world for cloud software application security. We maintain advanced open source security software solving authentication, authorization, access control, application network security, and delegation. Ory implements a variety of industry and best-practice standards including OAuth 2.0 / OAuth 2.1, OpenID Connect, Zero Trust Networking, Google Zanzibar Policy Framework, FIDO2 U2F, WebAuthn, TOTP, and more.

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Yes it you centralize login / authN on one cookie domain and do an OAuth2 integration into all the apps/other websites to do AuthCode Grant 

I just run the example code on the website and it work fine. but how to setup oauth2, any example to do that ?

my two website is like :    <https://mysite.com>   and  <https://sub.mysite.com>  , they are hosted on different  machine.
What I want is, if the user is already logged in at <https://mysite.com>, when he enters <https://sub.mysite.com>, there is no need to log in again.

as per the DM thread, subdomains are a non-issue