a.sql

SELECT *
FROM posts
INNER JOIN category_joins as filter_categories_join
  ON filter_categories_join.categorizable_id = posts.id 
  AND filter_categories_join.categorizable_type = 'Post'
INNER JOIN categories as filter_categories 
  ON filter_categories.id = filter_categories_join.category_id
INNER JOIN category_joins as categories_join_1
  ON categories_join_1.categorizable_id = posts.id
  AND categories_join_1.categorizable_type = 'Post'
INNER JOIN categories as categories_1
  ON categories_1.id = categories_join_1.category_id
INNER JOIN category_joins as categories_join_2
  ON categories_join_2.categorizable_id = posts.id
  AND categories_join_2.categorizable_type = 'Post'
INNER JOIN categories as categories_2
  ON categories_2.id = categories_join_2.category_id
WHERE filter_categories.lft BETWEEN 14 AND 115
  AND categories_1.lft BETWEEN 133 AND 134
  AND categories_2.lft BETWEEN 137 AND 138