There is indeed still nothing to be found either in Magento 1.x API guide either in the code.
You can clearly see in the folder structure of the Mage_Catalog
module that the model representing categories are still only sub models of the product, so it's main goal is still "only" to be able to know in which categories a specific product is linked to.
And the code of this category model being of class Mage_Catalog_Model_Api2_Product_Category_Rest
doesn't look like anything as changed from the previous answer, sadly (around line 61 in the latest version 1.9.2.4) :
protected function _retrieveCollection()
{
$return = array();
foreach ($this->_getCategoryIds() as $categoryId) {
$return[] = array('category_id' => $categoryId);
}
return $return;
}
And I am unsure if Magento is still going to put any effort in REST API on the version 1.x of the framework.
Although there seems to be hope in Magento 2.x API list listing those available methods :
DELETE /V1/categories/:categoryId
GET /V1/categories/:categoryId
POST /V1/categories
GET /V1/categories
PUT /V1/categories/:id
PUT /V1/categories/:categoryId/move
Also the code offers possibilities to get the categories tree.
See here and there.
So it is definitely something possible under Magento 2.x