Untitled

<html>
<head>
<script type="text/javascript" src="https://code.jquery.com/jquery-3.1.1.min.js"></script>
</head>
<body>
<select id="mySelect"></select>

<script>
    $.getJSON('categories.json', function(data) {
            // Очищение списка
            $('#mySelect').empty();
            for (var i = 0; i < data.length; i++) {
                $('#mySelect').append('<option value="'
                    + data[i].id + '">' + data[i].name + '</option>');
            }
        }
    );
</script>
</body>
</html>