Welcome to the QuickBooks Community, trains. Could you clarify where exactly you're having trouble adding the category column to your inventory? Are you currently looking at your main Products & services list, or are you trying to customize a specific inventory report?
If you’re working on the Products & services page, QuickBooks doesn't have a separate category column for your categories. Instead, you can organize them to appear as bold header rows. Just click the small Gear icon right above your list and check the Group by Category box.

For Inventory Valuation (Summary or Detail) reports, categories also work as grouping headers that sit right above your data rows. We can enable this by navigating to Customize, opening the Filter section, and selecting Product/Service > equals > tick your categories. The Physical Inventory Worksheet, on the other hand, allows you to enable the Category column directly through the standard customization settings.

Let me know if those steps do the trick or if you're looking for something else entirely.