UPDATE "#__categories" SET published = 1 WHERE alias = 'root';
UPDATE "#__categories" AS "c"
SET published = c2.newPublished
FROM (
SELECT c2.id, CASE WHEN MIN(p.published) > 0 THEN MAX(p.published) ELSE MIN(p.published) END AS newPublished
FROM "#__categories" AS "c2"
INNER JOIN "#__categories" AS "p" ON p.lft <= c2.lft AND c2.rgt <= p.rgt
GROUP BY c2.id) AS c2
WHERE c2.id = c.id;

UPDATE "#__menu" SET published = 1 WHERE alias = 'root';
UPDATE "#__menu" AS "c"
SET published = c2.newPublished
FROM (
SELECT c2.id, CASE WHEN MIN(p.published) > 0 THEN MAX(p.published) ELSE MIN(p.published) END AS newPublished
FROM "#__menu" AS "c2"
INNER JOIN "#__menu" AS "p" ON p.lft <= c2.lft AND c2.rgt <= p.rgt
GROUP BY c2.id) AS c2
WHERE c2.id = c.id;