Is there a way the category folder appear when you select assets instead of the files?

No, it is not possible to show specific category folder of asset on the asset Landing Page. The Categories are there to organize specific type of assets to a specific type of category. For example, if I have assets for Business Cards and it can only be used for Business Cards, the I can create for Business Cards and assign all the assets related to Business cards to this category. If you have an asset that can be used on multiple products, then you can add it in multiple categories.
The asset categories are not linked with user or site or group of users and hence it is not possible to show a specific category folder when the specific user accesses asset.