Since products can be assigned to several categories, I think that your concept may be slightly disabled if you do not download the collection for each category. What do you expect to see if there are several categories for this product?
Regardless of the category page, you can use the following:
$currentCat = $_product->getCategory();
To get all the categories this product belongs to:
$categories = $_product->getCategoryCollection(); foreach($categories as $_category) {
Hope this helps. Thanks,
Joe
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