well the schema that you have is correct, with that schema you could define the model like this:

public function category(){
    return $this->belongsTo("Category", "parent");
}

now for the routing thing it sound to me that you need to traverse the category tree backwards. And I wouldn't have that kind of routing

domain.com/parent_category/child_1/child_2/child_3/child_N/item_id

having to many '/' is bad practice for SEO. Instead I would provide a breadcrumbs navigation for each item, and the routing would be

domain.com/itemType/item 

easier for the bots to read.

To generate the breadcrumb type just go backwards on that category

//return a collection of categories
public function traverse_backwards(){
    $collection = array();
    $i = $this;
    while($i != NULL)
        //add category to collection
        $collection[] = $i;
        //go back one level
        $i = $i->Category::find($i->parent);
    }
    return $collection;
}

This code has not been tested, is just for showing the logic behind the solution.

please check my question out. http://laravel.io/forum/08-18-2014-should-i-rely-on-an-abstract-structure-when-doing-a-php-application

Thank you so much for your response! That's good insight into what the bots will read. I could keep the url's shorter. I will probably just use a pattern closer to what you suggest.

Thank you!