Edit form with current checkbox values

I have a database with 3 tables: links, categories and category_link. Each Link can have many Categories, each Category can have many Links and the lookup is in the category_link table.

When I come to edit a Link I want to be able to see what Categories it already has and then edit them. But, I cannot seem to get the ticks to show in the boxes, this is my code for the checkboxes (I've removed the layouts and css for readability):

@foreach ($categories as $category)
		<input 
           		id="{{$category->id}}" 
               	value="{{$category->id}}" 
               	aria-describedby="category-description" 
                name="categories[]"
                type="checkbox" 
               	@if (in_array($category->id, $link->categories->id) ? 'checked' : '') @endif
		>
		<label for="{{$category->id}}">{{$category->category}}</label>
@endforeach

I currently get this error:

Exception
Property [id] does not exist on this collection instance. 

I'm not sure what it should be to get it to work. Thanks