Welcome to the Community. I'm here to offer some insight for printing the category list in QuickBooks Online.
I can see why it would be beneficial to be able to print this particular list. Currently this isn't an option within the system, but the Product Development Team is constantly working to improve the product. I'll be sure to pass your feedback along to let them know you'd like to be able to print your category list.
In the meantime, I've got an article for you that explains using Product and Service categories in QBO. You can check it out here: https://quickbooks.intuit.com/community/Inventory-and-projects/Introduction-to-categories-in-Product....
I wish you and your business continued success. I'll be here if you have any additional questions. Take care.