One of the common situation, when you need to, connected PrestaShop categories to ebay store categories.
For Ebay Catalog, you need to list all products in a single category. But for ebay store you want to extend the number of categories.

Example:
PrestaShop categories
-T-Short
-- Category 1
---- Sub Category 1
---- Sub Category 2
-- Category 2

Ebay Catalog Categories
- T- Short

Ebay Store Categories
- Store Category 1
-- Store Sub Category 1
-- Store Sub Category 2
- Store Category 2

For correctly list product you need to create:

1) Category mapping where select that All PS categories T-Short + Category 1 + Sub Category 1 + Sub Category 2  + Category 2 -> send to ebay Catalog Category "T-Short"
2) Store Category Mapping
Where you create match
T-Short-> Category 1 => Store Category 1
T-Short-> Category 1 -> Sub Category 1 => Store Sub Category 1
T-Short-> Category 1 -> Sub Category 2 => Store Sub Category 2
T-Short-> Category 2 => Store  Category 1


This will send PrestaShop product from  category "T-Short->Category 1->Sub Category 2" to ebay Catalog category "T-Short" and also assign it to ebay store category "Store Category 1->Store Sub Category 2"