I would like to find out the highest quantity of the item of each category.

I have a table named "products" as shown below :

```
+----------+-------+-----+
| Category | Item  | Qty |
+----------+-------+-----+
| A        | A100  |  15 |
| A        | A100  |   7 |
| A        | A101  |   3 |
| A        | A101  |   9 |
| B        | B100  |   6 |
| B        | B100  |   7 |
| B        | B101  |   8 |
| B        | B101  |  13 |
+----------+-------+-----+

```

After I execute the query

```
SELECT Category, Item, SUM(Qty) as Quantity FROM products GROUP BY Category,Item;

```

I got the results as below

```
+----------+-------+----------+
| Category | Item  | Quantity |
+----------+-------+----------+
| A        | A100  |       22 |
| A        | A101  |       12 |
| B        | B100  |       13 |
| B        | B101  |       21 |
+----------+-------+----------+

```

Now I want to find the highest quantity of the item in each category, which I want to have my output as follows :

```
+----------+-------+----------+
| Category | Item  | Quantity |
+----------+-------+----------+
| A        | A100  |       22 |
| B        | B101  |       21 |
+----------+-------+----------+

```

how can I do that? I have tried the query below but I only got 'OK' as the result without giving me any output table. 

```
select Category, Item, max(Qty) as Quantity from products group by OD_type  having Quantity = (select sum(Qty) from products group by Item);

```

How can I get my desired output as shown in the table above? 
I am sorry if this is not a good question or my question is not clear enough.
Any help will be appreciated, Thank you!