Per-table dumps created with mysqldump and listed at: dumps.wikimedia.org/. Most notably, for the English Wikipedia: dumps.wikimedia.org/enwiki/latest/
A few of the files are not actual tables but derived data, notably dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz from Download titles of all Wikipedia articles
The tables are "documented" under: www.mediawiki.org/wiki/Manual:Database_layout, e.g. the central "page" table: www.mediawiki.org/wiki/Manual:Page_table. But in many cases it is impossible to deduce what fields are from those docs.
dumps.wikimedia.org/enwiki/latest/enwiki-latest-category.sql.gz contains a list of categories. It only contains the categories and some counts, but it doesn't contain the subcategories and pages under each category, so it is a bit pointless.
The SQL first defines the table:
CREATE TABLE `category` (
  `cat_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `cat_title` varbinary(255) NOT NULL DEFAULT '',
  `cat_pages` int(11) NOT NULL DEFAULT 0,
  `cat_subcats` int(11) NOT NULL DEFAULT 0,
  `cat_files` int(11) NOT NULL DEFAULT 0,
  PRIMARY KEY (`cat_id`),
  UNIQUE KEY `cat_title` (`cat_title`),
  KEY `cat_pages` (`cat_pages`)
) ENGINE=InnoDB AUTO_INCREMENT=249228235 DEFAULT CHARSET=binary ROW_FORMAT=COMPRESSED;
followed by a few humongous inserts:
INSERT INTO `category` VALUES (2,'Unprintworthy_redirects',1597224,20,0),(3,'Computer_storage_devices',88,11,0)
which we can see at: en.wikipedia.org/wiki/Category:Computer_storage_devices
Se see that en.wikipedia.org/wiki/Category:Computer_storage_devices_by_company
so it contains only categories.
We can check this with:
sed -s 's/),/\n/g' enwiki-latest-category.sql | grep Computer_storage_devices
and it shows:
(3,'Computer_storage_devices',88,11,0
(521773,'Computer_storage_devices_by_company',6,6,0
There doesn't seem to be any interlink between the categories, only page and subcategory counts therefore.