Create product catalog views page, and show child categories (taxonomy terms).
Create a Term view and set it to a block.
Select a format Grid/Table/etc..
Select the fields you want to show. Category name/image/etc...
Filter Criteria go with Taxonomy term: Vocabulary and select the vocabularies.
Now under Contextual filters
Taxonomy term: Parent term
Provide default value: Taxonomy Term ID from URL
Create a page shows products, and set path to /category/%1.
on Header choose the views >block.