Only some numbers.

As is, my implementation requires objects where "<" and "<=" are meaningful, and it requires that a comparison to -math.inf is also meaningful.

For example, it won't work with complex numbers, first because they cannot be compared to -math.inf:

  >>> list(monotonic_direct([1j, 2j, 4j]))
  Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    File "monotonic.py", line 40, in monotonic_direct
    test = prev_value <= value
  TypeError: '<=' not supported between instances of 'float' and 'complex'

and second because Python doesn't support an ordering for complex numbers:

  >>> 1j < 2j
  Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
  TypeError: '<' not supported between instances of 'complex' and 'complex'

As I mentioned, it's possible to replace the sentinel -math.inf with something that starts with seq[0]. This would allow strings and orderable objects.

This is left as an exercise for the reader. ;)