Some E-commerce platforms has thousands of products listed on them and some others have even crores of them. Product classification is important whether e-commerce platform lists hundred, thousand or a crore products. Product classification on e-commerce webpanies is generally done in the form of categories. There is generally a tree structure of categories where a category has branch category and then further branches and so on which means one child belongs to 1 parent category only and parent category can have multiple children branches (categories). In other cases there would be many to many mapping. A child category could belong to multiple parent categories and a parent category can have multiple child categories.
Different webpanies use one of the methods depending on the product classification. Niche product webpanies would often use former method and marketplaces/width product selling platforms would generally go for latter method. Because of variety in products when listing products there would be many products which would fit in multiple categories. And products are sometimes browsed by user based on category structure it becomes important to have many to many relationship.
Along with category classification, products should also be tagged. Tags could be used during search (making it efficient, fast, relevant) and on product detail display page as links. Tags could be category, brand name, attributes, property, product generic name.