In domain driven design, can entities have their own repositories?

IMHO, in your Domain Model, Category should not be child of the Product Aggregation. The Product has a Category, but it does not know how to create or edit a Category.

Placing something You don't know where to put into artificial services usually leads to anemic domain model.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.