Post Filtering by GET URL parameters

You have to filter the posts in the query arguments.

Try:

$mycat = $_GET['category'];

$arg = array(
        'type' => 'post',
        'order' => 'ASC',
        'category_name' => $mycat
    );

Just remove the square brackets from the link, or use: $mycat[0]

$mycat = $_GET['category'];

$arg = array(
        'type' => 'post',
        'order' => 'ASC',
        'category_name' => $mycat[0]
    );