Overwrite category head title

You can use the wp_title filter to modify the output of the wp_title function.

quick example based on the example from Codex:

add_filter( 'wp_title', 'wpa66574_title_filter', 10, 3 );

function wpa66574_title_filter( $title, $sep, $seplocation ) {
    // account for $seplocation
    $left_sep = ( $seplocation != 'right' ? ' ' . $sep . ' ' : '' );
    $right_sep = ( $seplocation != 'right' ? '' : ' ' . $sep . ' ' );

    $page_type="";

    // get special page type (if any)
    if( is_category( 'videos' ) ) $page_type = $left_sep . 'Archive' . $right_sep;

    // get the page number
    if( get_query_var( 'paged' ) ) $page_num = $left_sep. get_query_var( 'paged' ) . $right_sep; // on index
    elseif( get_query_var( 'page' ) ) $page_num = $left_sep . get_query_var( 'page' ) . $right_sep; // on single
    else $page_num = '';

    // concoct and return title
    return $page_type . $title . $page_num;
}