Subquery caching in join

Question

I have very complex MySQL queries that use the same subquery over and over again. I was wondering if MySQL will run the subquery multiple times or use the previous resultset. Is there any way to tell MySQL to save or cache the results?

My query is as follows:

SELECT
    pc.categoryId,
    COUNT(pc.productId)
FROM
    product_categories pc
INNER JOIN
    (
    SELECT
        t1.productId AS s1
    FROM
        product_categories t1
    JOIN
        product_highlights t2
    ON
        t1.productId = t2.productId
    WHERE
        t1.categoryId IN(7, 5) AND t2.highlightId IN(9, 10, 11)
    GROUP BY
        t1.productId
    HAVING
        2 * 3 = COUNT(
            DISTINCT t1.categoryId,
            t2.highlightId
        )
) productsIds
ON
    pc.productId = productsIds.s1
GROUP BY
    pc.categoryId

UPDATE:

Here is EXPLAIN query:

+----+-------------+------------+------------+-------+---------------+---------+---------+------+------+----------+-----------------------------------------------------------------+
| id | select_type | table      | partitions | type  | possible_keys | key     | key_len | ref  | rows | filtered | Extra                                                           |
+----+-------------+------------+------------+-------+---------------+---------+---------+------+------+----------+-----------------------------------------------------------------+
|  1 | PRIMARY     | <derived2> | NULL       | ALL   | NULL          | NULL    | NULL    | NULL |    4 |   100.00 | Using temporary; Using filesort                                 |
|  1 | PRIMARY     | pc         | NULL       | index | PRIMARY       | PRIMARY | 4       | NULL |    5 |    20.00 | Using where; Using index; Using join buffer (Block Nested Loop) |
|  2 | DERIVED     | t1         | NULL       | index | PRIMARY       | PRIMARY | 4       | NULL |    5 |    80.00 | Using where; Using index; Using temporary; Using filesort       |
|  2 | DERIVED     | t2         | NULL       | index | PRIMARY       | PRIMARY | 4       | NULL |    7 |    14.29 | Using where; Using index; Using join buffer (Block Nested Loop) |
+----+-------------+------------+------------+-------+---------------+---------+---------+------+------+----------+-----------------------------------------------------------------+
4 rows in set, 1 warning (0.00 sec)

SQL Fiddle of my database.

UPDATE 2:

Temporary table query:

CREATE TEMPORARY TABLE IF NOT EXISTS tempProducts
(
    tmpProductId SMALLINT NOT NULL,
    PRIMARY KEY(tmpProductId)
) ENGINE = MEMORY 

SELECT
    t1.productId AS tmpProductId
FROM
    product_categories t1
JOIN product_highlights t2 ON
    t1.productId = t2.productId
WHERE
    t1.categoryId IN(7, 5) AND t2.highlightId IN(9, 10, 11)
GROUP BY
    t1.productId
HAVING
    2 * 3 = COUNT(
        DISTINCT t1.categoryId,
        t2.highlightId
    );

Temp table will look like:

+--------------+
| tmpProductId |
+--------------+
|            1 |
|            2 |
+--------------+

> show index from tempProducts where Key_name = 'PRIMARY'

+--------------+------------+----------+--------------+--------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| Table        | Non_unique | Key_name | Seq_in_index | Column_name  | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment | Index_comment |
+--------------+------------+----------+--------------+--------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| tempproducts |          0 | PRIMARY  |            1 | tmpProductId | NULL      |           2 |     NULL | NULL   |      | HASH       |         |               |
+--------------+------------+----------+--------------+--------------+-----------+-------------+----------+--------+------+------------+---------+---------------+

UPDATE 3:

Query with temporary table:

SELECT
    categoryId,
    COUNT(productId)
FROM
    product_categories tb1
INNER JOIN tempProducts tb2 ON
    tb1.productId = tb2.tmpProductId
GROUP BY
    categoryId;

I added composite UNIQUE index to product_categories table: UNIQUE(productId, categoryId)

EXPLAIN query:

+------+-------------+-------+--------+-----------------------------+---------+---------+------------------+------+-------------+
| id   | select_type | table | type   | possible_keys               | key     | key_len | ref              | rows | Extra       |
+------+-------------+-------+--------+-----------------------------+---------+---------+------------------+------+-------------+
|    1 | SIMPLE      | tb1   | index  | productId_categoryId_unique | PRIMARY | 4       | NULL             |    5 | Using index |
|    1 | SIMPLE      | tb2   | eq_ref | PRIMARY                     | PRIMARY | 2       | ss.tb1.productId |    1 |             |
+------+-------------+-------+--------+-----------------------------+---------+---------+------------------+------+-------------+