def list_to_indexed_dict(list_: list) -> dict:
    """
    Map a list of objects to a sorted dict of indexes.

    Assign indexs to distinct objects in a list and return a dictionary with
    keys in range(num unique objects) maping to the object.

    Args:
        list_ (list): A list of objects to index.

    Returns:
        dict: Sorted dictionary indexing unique objects in input list.
    """
    return dict(enumerate(sorted(set(list_))))