Bringing object records into WordPress is what CultureObject does, but once the records are in there, you’ll need a way of displaying them on your site.
This is done in exactly the same way you’d do it for any other Custom Post Type – you run a standard WordPress Loop against the object post type, use pagination, object-single.php, searches, the in-built WordPress archive hierarchy and so on in order to display, filter and search your object records on your site.