In your Axios
Add catch for the error
axios.put('category/'+id,data,{ headers: { 'Content-Type': 'multipart/form-data' } })
.then(res=>{
console.log(res);
}),catch(res=>{
console.log('error',res);
});
Controller
You should return the $category instead of $request
public function update(Request $request, $id)
{
$category = Category::find($id);
return $category;
}