I assume you want to search your array for elements that match certain criteria.
I've included a method to search for fonts by variant or variants.
<?php
$fonts =
[
    [
        'family'   => 'Foo',
        'category' => 'sans-serif',
        'variants' =>
            [
                'regular',
                'italic'
            ]
    ],
    [
        'family'   => 'Bar',
        'category' => 'cursive',
        'variants' =>
            [
                'regular',
                'bold'
            ]
    ],
    [
        'family'   => 'Baz',
        'category' => 'monospace',
        'variants' =>
            [
                'italic',
                'regular',
                'bold'
            ]
    ]
];
// Build some indexes for search functions.
$family_index   = [];
$variants_index = [];
foreach($fonts as $index => $font) {
    $family_index[$font['family']] = $index;
    foreach($font['variants'] as $variant) {
        $variants_index[$variant][] = $index;
    }
}
$filter_by_family = function($family) use ($fonts, $family_index) {
    return isset($family_index[$family]) ? $fonts[$family_index[$family]] : null;
};
$filter_by_variants = function(array $variants) use ($fonts, $variants_index) {
    $font_index_matches = array();
    foreach($variants as $variant) {
        if(isset($variants_index[$variant])) {
            $font_index_matches[] = $variants_index[$variant];
        }
    }
    if(!count($font_index_matches)) return;
    $matches = count($font_index_matches) > 1 
        ? call_user_func_array('array_intersect', $font_index_matches)
        : $font_index_matches[0];
    return array_intersect_key($fonts, array_flip($matches));
};
var_dump($filter_by_family('Bar'));
var_dump($filter_by_variants(['italic']));
var_dump($filter_by_variants(['regular','bold']));
Output:
array (size=3)
  'family' => string 'Bar' (length=3)
  'category' => string 'cursive' (length=7)
  'variants' => 
    array (size=2)
      0 => string 'regular' (length=7)
      1 => string 'bold' (length=4)
array (size=2)
  0 => 
    array (size=3)
      'family' => string 'Foo' (length=3)
      'category' => string 'sans-serif' (length=10)
      'variants' => 
        array (size=2)
          0 => string 'regular' (length=7)
          1 => string 'italic' (length=6)
  2 => 
    array (size=3)
      'family' => string 'Baz' (length=3)
      'category' => string 'monospace' (length=9)
      'variants' => 
        array (size=3)
          0 => string 'italic' (length=6)
          1 => string 'regular' (length=7)
          2 => string 'bold' (length=4)
array (size=2)
  1 => 
    array (size=3)
      'family' => string 'Bar' (length=3)
      'category' => string 'cursive' (length=7)
      'variants' => 
        array (size=2)
          0 => string 'regular' (length=7)
          1 => string 'bold' (length=4)
  2 => 
    array (size=3)
      'family' => string 'Baz' (length=3)
      'category' => string 'monospace' (length=9)
      'variants' => 
        array (size=3)
          0 => string 'italic' (length=6)
          1 => string 'regular' (length=7)
          2 => string 'bold' (length=4)