How to create a nested array from current array in PHP?

I am trying to read the categories in an XML file from my API provider. The only problem is that they nested the subcategories in a string:

[
{category: "root|sub|another_sub"},
{category: "root|sub2},
{category: "sibling|sub|foo"),
{category: "root|sub|foo")
]

I need to display the above data in a nested html list like:

<li>
  root
  <ul>
    <li>sub 
      <ul>
        <li>another_sub</li>
      </ul> 
      <ul>
        <li>foo</li>
      </ul>
    </li>
    <li>sub 2</li>
  </ul>
  <li>sibling
    <ul>
      <li>sub
        <ul>
          <li>foo</li>
        </ul>
      </li>
    </ul>
</li>

I literally can't think of a solution to do this dynamically.. I tried using multiple loops and array_reduce but no success. Can someone explain how this works?