Order by and limit on a multiple left join - PostgresSQL and python - sql

Question

I have the following relations:
A Product have multiple Images
A Product can have multiple Categories
A Category can have multiple Products
I want to get:
only the 'short_name' from the first category
only the first image url order_by another parameter
I have the following SQL, in PostgreSql:
SELECT DISTINCT ON(I.product_id) P.id, P.name, P.short_description,
CAT.short_name AS category, I.url
FROM products_product AS P
LEFT JOIN products_product_categories AS RPC ON P.id = RPC.product_id
LEFT JOIN categories_category AS CAT ON RPC.category_id = CAT.id
LEFT JOIN products_productimage AS I ON I.product_id = P.id
WHERE (P.is_active = TRUE)
My issue is that I don't know to limit left join and order by, I try to add LIMIT 1
LEFT JOIN categories_category AS CAT ON RPC.category_id = CAT.id LIMIT 1
but it is not working, I receive a code error 'syntax error at or near "LEFT"'
Category table
id | category_name | category_short_name
1 catA A
2 catB B
3 catC C
Product table
id | product_name | product_desc
1 P1 lorem1
2 P2 lorem2
3 P3 lorem3
ManytoMany: product_category
id product_id category_id
1 1 1
2 2 1
3 1 2
4 3 3
5 3 3
Image table
id url product_id order
1 lo1 1 4
2 lo2 1 0
3 lo3 1 1
4 lo4 2 0
For Product with id1 I expect to get:
name: P1, desc 'lorem1', category short_name : cat A, image url lo2

Answer 1

DISTINCT ON makes no sense without ORDER BY. As you want two different orders (on i.order for images and on cat.id for categories), you must do this in separate subqueries.
select p.id, p.name, p.short_description, c.short_name, i.url
from products_product p
left join
(
select distinct on (pcat.product_id) pcat.product_id, cat.short_name
from products_product_categories pcat
join categories_category cat on cat.id = pcat.category_id
order by pcat.product_id, cat.id
) c on c.product_id = p.id
left join
(
select distinct on (product_id) product_id, url
from products_productimage
order by product_id, order
) i on i.product_id = p.id
where p.is_active
order by p.id;
Two alternatives to write this query are:
subqueries with fetch first row only in the select clause
lateral left joins on subqueries with fetch first row only