获取用户选择的类别的ID

Question

我从类别表中获取了ID和名称，并在下拉列表中查看了所有名称，选择名称后，我想将该名称的ID作为外键存储在产品表中

这是我的功能

public function create()
{
    $category = category::pluck('name','id');
    return view ('books.addbook',compact('category'));
}
public function store(Request $request)
{
    $this->validate($request,[
        'category'=>'required',            
    ]);
    books::create($request->all());
}

这是视图

<div class="form-group row">
    <label for="colFormLabelLg" class="col-form-label col-form-label-lg">category</label>
    <select class="col-sm-10" name ="category">
    <option ></option>          

    @foreach($category as $cat)
    <option class="col-sm-10" value="{{$cat}}" name ="category" class="form-control form-control-lg" >{{$cat}}</option>          
    @endforeach
    </select>
</div>
</div>

我如何仅存储类别的ID？