Displaying posts based on category

Add category_name or cat in your arguments (args) array.

<div id="mini_stream">
    <ul>
<? $args = array(
    'post_type' => 'post',
    'posts_per_page' => 4,
    'category_name'=>'html',
);

$loop = new wp_Query($args);

while($loop->have_posts()) : $loop->the_post();
    echo '<a href="'.get_permalink().'">';
    echo get_the_post_thumbnail($post->ID, 'category-thumb');
    the_title( '<h6>', '</h6>' );
    echo '</a>';
endwhile;

wp_reset_query(); ?>
    </ul>
</div>