>Imagine situation we want to find MIN value. But we can do nothing just with value, we need ID of record that contains MIN value. In VFP I can write
>SELECT MIN(MyNumber), ID_FIELD, category from Mytable group by category.
>

Actually, this would contain ID of record that contains *one of the records* that satisfies the MIN() condition. There may be only one record that has the MIN(mynumber), but there may be more.

You would need to group by category and id_field to get the true MIN(mynumber).
Since the lowest MIN(mynumber) of category+id_field will be the lowest MIN(mynumber) of category alone anyway, you use TOP to get the records with the lowest value of MIN(mynumber) from that group e.g.

SELECT TOP 1 category, id_field, MIN(mynumber) 
  FROM mytable 
  GROUP BY category, id_field
  ORDER BY 3

If there is more than one record in the result set, then there is more that one category+id_field combination that has that MIN(mynumber).