We can associate google, Twitter, or any Oauth2.0 authorisation with AWS cognito. But, can we use our cognito as Oauth2.0 or an identity provider for other websites?
Amazon Cognito is an OIDC provider. So if website supports OIDC, you can use Cognito as an identity provider. You can find more details about OIDC configurations here: http://docs.aws.amazon.com/cognito/latest/developerguide/amazon-cognito-user-pools-using-tokens-with-identity-providers.html