Laravel: не может показать отношения "многие-ко-многим"

В вашем случае есть нет надобности для определения ВыставкаHasArt. Документация от laravel many to many.

Здесь я пробовал изменять ваши коды напрямую, только для выражения логики «многие ко многим», поэтому вам, возможно, придется отлаживать их и самостоятельно настраивать вашу базу данных.

В моделях:

class Exhibition extends Model
{
    protected $table = 'exhibitions';
    //While the primary key of a table is set auto increasing, it doesn't need to be fillable.
    protected $fillable = [/*'Ex_id'*/,'Name','Start_date','End_date','Limit_visit','picture'];
    protected $primaryKey = 'Ex_id';

    public function art_objs() {
        //use "belongsToMany" instead of "belongsTo".
        return $this->belongsToMany(Art_obj::class, 'exhibition_has_art_objs', 'exhibition_id', 'art_obj_id_no');
    }
}

class Art_obj extends Model
{
    protected $table = 'art_objs';
    //The primary key of a table is usually set auto increasing, no need to be fillable.
    protected $fillable = [/*Id_no, */'Type_of_art','Type_of_coll','Picture']; 
    protected $primaryKey = 'Id_no';

    public function exhibitions() {
        return $this->belongsToMany(Exhibition::class,'exhibition_has_art_objs', 'art_obj_id_no', 'exhibition_id');
    }
}

В ExhibitionController:

public function show($Ex_id)
{
    $exhibition = Exhibition::find($Ex_id);
    return view('Exhibition.ShowExhibition', compact('exhibition')); 
}

Ввиду:

<h1>Exhibition: {{$exhibition->Ex_id}}</h1>
<h2>Art objects in this exhibition</h2>
<br>
<table class = "table table-bordered table-striped"> 
    <tr>
        <td>exhibition_id</td>
        <td>art_obj_Id_no</td>
        <td>Title</td>
    </tr>
    @foreach($exhibition->art_objs as $art_obj) 
        <tr>
            <td>{{$exhibition->Ex_id}}</td>
            <td>{{$art_obj->Id_no}}</td>
            <td>{{$art_obj->Type_of_art}}</td>
        </tr>
    @endforeach 
</table>

вы должны изменить свои отношения таким образом, если вам действительно нравится получать данные из сводной таблицы

please let me know if i am wrong.

Выставочная модель:

class Exhibition extends Model
{
    protected $table = 'exhibitions';
    protected $fillable = ['Ex_id','Name','Start_date','End_date','Limit_visit','picture'];
    protected $primaryKey = 'Ex_id';

    public function ExhibitionHasUser(){
        return $this->hasMany(ExhibitionHasUser::class,'exhibition_id','Ex_id');
    }
}

ВыставкаHasArt Model

class ExhibitionHasArt extends Model
{
    protected $table = 'exhibition_has_art_objs';
    protected $fillable = ['list_no','exhibition_id','art_obj_Id_no'];
    protected $primaryKey = 'list_no';

    public function Exhibition(){
        return $this->belongsTo(Exhibition::class,'exhibition_id', 'Ex_id');
    }

    public function Art_obj(){
        return $this->belongsTo(Art_obj::class,'art_obj_Id_no', 'Id_no');
    }
}

Art_obj Модель

class Art_obj extends Model
{
    protected $table = 'art_objs';
    protected $fillable = ['Id_no','Type_of_art','Type_of_coll','Picture'];
    protected $primaryKey = 'Id_no';


    public function ExhibitionHasArt(){
        return $this->hasMany(ExhibitionHasArt::class,'art_obj_Id_no','Id_no');
    }
}