From my point of view, your fix in reality does not seems to fix it. Yes, you have incorporated standalone Category entity which is good thing, but lets say I have 10 categories named "cat1", "cat2", "cat3" ... "cat10".

With your fix, there are 3 tables

1) Installation table
2) Installation_Category table which has two attributes, "Installation_id" and "categories_id".
3) Category table, which has "id" and "name" attributes.

What it does right now is that "categories_id" in Installation_Category table maps to "id" in "Category" table.

When I have 1000 categories and I assign e.g. 50 categories from these 1000 to some installation, even I pick category with the same name, it is considered as totally new category.

So in the end, I have this in Category table:

id     name
1      cat1
2      cat1
3      cat2
4      cat1

I want it like this

1    cat1
2    cat2

So in that Installation_Category table I want it to have like this

Installation_id    categories_id
uuid1                   1
uuid1                   2
uuid1                   3
uuid2                   2  
uuid3                   1

instead of this

uuid1                   1
uuid1                   2 
uuid1                   3
uuid1                   4
uuid2                   5
uuid3                   6
uuid4                   7
uuid5                   8

In other words, category should be unique according to its name. It does not make sense at all to have multiple categories with same names - it solves nothing regarding perfomance and database storing effectivity since it generates new category every time.