The main category determines the canonical URL and breadcrumbs for products. In order for a product to be visible in the store, it must have a main category assigned to it. Each category is designed to have one main category assigned to it.
To select the main category for a product, simply choose from the available options in the Category dropdown located within the Product Categories box in the product view.
If a category that is assigned as the main category on a product is set to inactive, any product using that category as its main category will automatically become unpublished.
To republish the product, you must assign a new main category to it.