>So I immediately hit a block as I'm struggling to understand why I need the notion of a Functor to understand what in the end looks like just lazy mapping of a

>So I immediately hit a block as I'm struggling to understand why I need the notion of a Functor to understand what in the end looks like just lazy mapping of a function over a stream. What you're calling "lazy mapping a function over a stream" is an example of a functor. To be precise the functor goes from "type a" to "stream of type a" (note that this isn't quite the same as a function since it operates on the level of types). You don't need to understand Functors to understand how mapping over a stream works, however if you understand mapping over a stream then you can understand any other functor as being similar to mapping over a stream. Now functors are somewhat basic so it's hard to come up with a really nontrivial example, but you could for instance consider: generate_b = lambda: function_a_to_b(generate_a()) to be pretty much the same thing as mapping over a stream, even though those functions can't be iterated over and could just be generating random data, or sample some time series etc. Note that here we're transforming the output, when you start transforming the input you get something contravariant, like when you do something as follows: class CoMapped: # ... # def __index__(self, a): return self.object_with_b_index[self.function_a_to_b(a)] it looks a bit weird to do this in Python though as there's no way to denote types.