Get tags specific category

If you use get_terms(), then you can retrieve all terms for a given taxonomy (this includes category as well as post-tag).

To get the category on a category archive page, you can use

get_category( get_query_var( 'cat' ) )

which will give you an object of the currently displayed cat archive page.

So the actual term list will be available with something like the following:

$terms = get_terms(
     get_category( get_query_var( 'cat' ) )
    ,array(
         'fields'       => 'ids'
        ,'hierarchical' => true
        ,'hide_empty'   => false
        ,'pad_counts'   => true
     )
);

$term_links = array();
foreach ( $terms as $term )
{
    $link = get_term_link( $term, $taxonomy );

    ! is_wp_error( $link ) AND $term_links[] = sprintf(
             '<a href="https://wordpress.stackexchange.com/questions/75017/%s" rel="tag">%s</a>'
            ,esc_url( $link )
            ,$term->name
    );
}
// Now do something clever with $term_links
// For example:
! is_empty( $terms ) AND printf(
     '<ul>%s</ul>'
    ,implode( "", $term_links )
);