Hope you did pretty url on your site already (Settings>Permalinks). If so, Let’s guess your Category base is blank there.
You have to add Custom posts in category archive using a filter. To do so, add this to function.php:
function go_add_custom_types( $query ) {
if( is_category() || is_tag() && empty( $query->query_vars['suppress_filters'] ) ) {
$query->set( 'post_type', array(
'post', 'nav_menu_item', 'your-custom-post-type-here'
));
return $query;
}
}
add_filter( 'pre_get_posts', 'go_add_custom_types' );
In default setup, WordPress Structure act like this (Based on observation on my blog)
For Default category,
site.com/category/catgory-name
or site.com/category-name
For custom taxonomy (by chance)
site.com/custom-taxonomy-slug/category-name
For single news (CPT)
site.com/news/post-name.
For single Default post:
site.com/<depends-on-permalink-structure>