recursion2.js

let categories = [
  {id: 'animals', 'parent': null},
  {id: 'mammals', 'parent': 'animals'},
  {id: 'dogs', 'parent': 'animals'},
  {id: 'chihuahua', 'parent': 'dogs'},
  {id: 'labrador', 'parent': 'dogs'},
  {id: 'persian', 'parent': 'cats'},
]



let makeTree = (categories, parent) => {
  let node = {}
  categories
    .filter(c => c.parent === parent)
    .forEach(c => 
      node[c.id] = makeTree(categories, c.id)) 
  return node
}



console.log(
  JSON.stringify(
  makeTree(categories, null)
  , null, 2)
)

/* output
{
  "animals": {
    "mammals": {},
    "dogs": {
      "chihuahua": {},
      "labrador": {}
    }
  }
}
*/