The search properties module allows you to add various properties. However, you might want to enable search through categories. Category is not a property, so you can't add it to your search properties by default.
You can solve this by creating a derived property from the direct category. The direct category is just the category that is linked to the product, without all the categories above.
Voorbeeld:
The direct category of the product above is Accessories. Tweakwise and Root are not included in this derived property.
Read how to create this derived property in How do I create a derived property 'Direct category'?