JavaScript Creating a new array from recursive mapping

[tdev81]

I am attempting to do something very complex.

I have a database that has a self relation (categories that contain a nested category).
The ORM I’m using makes use of these categories as objects:

category = [
  {
    name: "Lights",
    description: "some description",
    parentid: "some id",
    children: [
         [{name: "bulbs", description: "some description", parentid: "some id", children: [...more children]}]
         [{name: "LEDs", description: "some description", parentid: "some id", children: [...more children]}]
         [{name: "CFL", description: "some description", parentid: "some id", children: [...more children]}]
                  ]
  },
  {
    name: "Cats",
    description: "some description",
    parentid: "some id",
    children: [
         [{name: "brown", description: "some description", parentid: "some id", children: [...more children]}]
         [{name: "white", description: "some description", parentid: "some id", children: [...more children]}]
         [{name: "gray", description: "some description", parentid: "some id", children: [...more children]}]
                  ]
  },
]

I’m wanting to output a new array of objects that look like this:

newArray = [
     {name: "Lights", lastChildId: "someid"},

     {name: "Lights > bulbs", lastChildId: "someid"},
     {name: "Lights > bulbs > *more children names...*", lastChildId: "someid"},

     {name: "Lights > LEDs", lastChildId: "someid" },
     {name: "Lights > LEDs > *more children names...*", lastChildId: "someid" },

     {name: "Lights > CFL", lastChildId: "someid"},
     {name: "Lights > CFL   > *more children names...*", lastChildId: "someid"},

     {name: "Cats", lastChildId: "someid"},
     {name: "Cats > brown > *more children names...*", lastChildId: "someid"},

     {name: "Cats > white > *more children names...*", lastChildId: "someid" },
     {name: "Cats > gray  > *more children names...*", lastChildId: "someid"},
   ]

Basically I want to output a name of the complete path through the nested category names, but also outputting the intermediate steps between nesting (ie. even though one category might go Cats > Brown > Short, I want the array to contain all 3 different variations: Cats, Cats > Brown, Cats > Brown > Short.

This is going to be output in a drop down select list.

I understand this is super complex so I am not expecting someone to figure this out very quickly.