MySQL to List the types of objects within each schema.

SELECT ROUTINE_SCHEMA AS db, ROUTINE_TYPE AS object_type, COUNT(*) AS count
  FROM INFORMATION_SCHEMA.ROUTINES
 GROUP BY ROUTINE_SCHEMA, ROUTINE_TYPE
UNION
SELECT TABLE_SCHEMA, TABLE_TYPE, COUNT(*)
  FROM INFORMATION_SCHEMA.TABLES
 GROUP BY TABLE_SCHEMA, TABLE_TYPE
UNION
SELECT TABLE_SCHEMA, CONCAT('INDEX (', INDEX_TYPE, ')'), COUNT(*)
  FROM INFORMATION_SCHEMA.STATISTICS
 GROUP BY TABLE_SCHEMA, INDEX_TYPE
UNION
SELECT TRIGGER_SCHEMA, 'TRIGGER', COUNT(*)
  FROM INFORMATION_SCHEMA.TRIGGERS
 GROUP BY TRIGGER_SCHEMA
UNION
SELECT EVENT_SCHEMA, 'EVENT', COUNT(*)
  FROM INFORMATION_SCHEMA.EVENTS
 GROUP BY EVENT_SCHEMA
 ORDER BY DB, OBJECT_TYPE;