Q:

How can I extend the category products Rest API?

/V1/categories/(cat ID)/products
This API provides very less detail of all the products. 
{
    "sku": "Nike 3 color half sleeve tshirt",
    "position": 1,
    "category_id": "3"
  },
  {
    "sku": "Louis Phillipe Blue Jean Size 32",
    "position": 1,
    "category_id": "3"
  },
  {
    "sku": "Louis Phillipe Shirt Size M",
    "position": 1,
    "category_id": "3"
  },
  {
    "sku": "UCB shirt Size ",
    "position": 1,
    "category_id": "3"
  },

I can use the sku in a search filter to get all the produts with these sku's. But is there a better way around ?

A:

It is possible to use filter by category_id during request to Product Repository: 
GET <base_url>/rest/V1/products
If it is necessary to filter by store_id or website_id at the same time, see workaround here.

