Using multiple variables to assign categories to an array

To make an array, separate your values with commas rather than concatenate them with periods.

$upostcat= array (
  $video,
  $image,
  $audio,
  $writing,
  $event
);

That part is pure PHP. However, I notice you want to use the category_name “array”. If you are talking about WP_Query, category_name does not accept an array– really this is the only WordPress part of your question, by the way. What you actually want is a string with values separated by commas, like this from the Codex:

$query = new WP_Query( 'category_name=staff,news' );

For that you do need to concatenate. What you’ve done should mostly work except that you have a high probability of having a trailing comma. Imagine that one or more of the first four are set and the last one isn’t. There is an easier way.

if (isset($_POST['showvideo']) && ($_POST['showvideo'] == 'true')) {
    $cats[]='user-video';
} 
if (isset($_POST['showimage']) && ($_POST['showimage'] == 'true')) {
    $cats[]='user-image';
} 
if (isset($_POST['showaudio']) && ($_POST['showaudio'] == 'true')) {
    $cats[]='user-audio';
} 
if (isset($_POST['showwriting']) && ($_POST['showwriting'] == 'true')) {
    $cats[]='user-writing';
} 
if (isset($_POST['showevent']) && ($_POST['showevent'] == 'true')) {
    $cats[]='user-event';
};
if (!empty($cats)) {
  $upostcat = implode(',',$cats);
}

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