If yes, you just need to create a simple lookup from your Categories Table to your Summary (there’s no need for a formula there) … And then select a category per row …
OK then the solution is to remove the third table and merge the results into your first. Since you want to know the sum of the values per category, the best place for this is in the originating Categories Table.
Create a column Value Sum and set it equal to: [Items Table].filter([Assigned Category]=thisrow).[value].sum()