Are Catalog/Categories & Item Relationships only maintained at Item Master Orgs?

Hello,

In Product Information Management (PIM): Are Catalog/Categories & Item Relationships only maintained at Item Master Orgs & then flow down to the associated child organizations upon any update to the item master?

Through my testing I noted that for Categories:

• I was only able to delete categories at the Item Master Org level - the 'x' was grayed out at the child orgs
• I was able to click the '+' icon to create a new category and see all my catalog/category options at the Item Master level, at the child level the dropdown was blank

Through my testing I noted that for Relationships