Polynomial functor
So, imagine you have a box of toys, and each toy has a number written on it. You can pick out any toy and look at the number on it.
Now, let's say you have a magic machine that can take those numbers and do some math with them. It can add them, subtract them, multiply them, and do all sorts of cool stuff.
That magic machine is like a polynomial functor. The toy numbers are like the "input" to the functor, and the math operations are like the "output" of the functor.
Basically, a polynomial functor is a way of taking some input (like toy numbers) and doing some math with them using a set of pre-defined operations (like adding and subtracting). It's like a magic math box that can turn one thing into another, just like turning toys into answers using math.
Now, let's say you have a magic machine that can take those numbers and do some math with them. It can add them, subtract them, multiply them, and do all sorts of cool stuff.
That magic machine is like a polynomial functor. The toy numbers are like the "input" to the functor, and the math operations are like the "output" of the functor.
Basically, a polynomial functor is a way of taking some input (like toy numbers) and doing some math with them using a set of pre-defined operations (like adding and subtracting). It's like a magic math box that can turn one thing into another, just like turning toys into answers using math.