Count how many posts in category

This is what I’m trying to do:

if number of posts is greater than 20 -> display link to another page (which shows all posts)
if number of posts is less than 20 -> don’t display the link

So far I’ve been able to return the number of posts using

$count_posts = wp_count_posts('inventory');
$published_posts = $count_posts->publish;

but I don’t know where to go from here, any suggestions?

If I remember right count of posts in category is stored persistently in category object. So use get_category() or variation of it and fetch the number out of object.

Example code (not tested):

$category = get_category($id);
$count = $category->category_count;

if( $count > $something ) {

    // stuff
}