code: def _compare(
      left: IndexOpsLike,
      right: Any,
      func_name: str,
      *,
      is_equality_comparison: bool = False,
  ) -> SeriesOrIndex:
      """
      Compare a Categorical operand `left` to `right` with the given Spark Column function.
  
      Parameters
      ----------
      left: A Categorical operand
      right: The other operand to compare with
      func_name: The Spark Column function name to apply
      is_equality_comparison: True if it is equality comparison, ie. == or !=. False by default.
  
      Returns
      -------
      SeriesOrIndex
      """
      if isinstance(right, IndexOpsMixin) and isinstance(
          right.dtype, CategoricalDtype
      ):
          if not is_equality_comparison:
              if not cast(CategoricalDtype, left.dtype).ordered:
                  raise TypeError(
                      "Unordered Categoricals can only compare equality or not."
                  )
          # Check if categoricals have the same dtype, same categories, and same ordered
          if hash(left.dtype) != hash(right.dtype):
              raise TypeError(
                  "Categoricals can only be compared if 'categories' are the same."
              )
          if cast(CategoricalDtype, left.dtype).ordered:
              return pyspark_column_op(func_name, left, right)
          else:
              return pyspark_column_op(
                  func_name, _to_cat(left), _to_cat(right)
              )
      elif not is_list_like(right):
          categories = cast(CategoricalDtype, left.dtype).categories
          if right not in categories:
              raise TypeError(
                  "Cannot compare a Categorical with a scalar, which is not a category."
              )
          right_code = categories.get_loc(right)
          return pyspark_column_op(func_name, left, right_code)
      else:
          raise TypeError(
              "Cannot compare a Categorical with the given type."
          )
  
imports: from itertools import chain
  from typing import cast, Any, Union
  import pandas
  import numpy
  from pandas.api.types import is_list_like, CategoricalDtype
  from pyspark.pandas._typing import Dtype, IndexOpsLike, SeriesOrIndex
  from pyspark.pandas.base import IndexOpsMixin
  from pyspark.pandas.data_type_ops.base import _sanitize_list_like, DataTypeOps
  from pyspark.pandas.typedef import pandas_on_spark_type
  from pyspark.sql import functions
  from pyspark.sql.utils import pyspark_column_op
label_desc: Use image node_id 1 for calling a global function with example usage: _compare(left, right, func_name) and returns: pyspark_column_op, pyspark_column_op, pyspark_column_op