How were the protagonist and co. able to take out real items and money from the world of cognition?

Solution 1:

I believe Morgana provides an explanation when it first happens. It simply works on the basis of “this is fiction deal with it” but it still has some backing too it. Pulling items out of the cognitive world would only be possible if they are there in the real world, although this cognitive world shows different properties to what we would think. If you consider persona 3’s dark hour (I won’t get into it too much incase you haven’t played the game) it’s a perfectly logical idea and totally plausible (to an extent) until you dig into it and start thinking about it more. An entire separate world simply created and controlled by our cognition that only a few are aware off? Plausible (to an extent) but when we think about it more it becomes unrealistic, like the treasure manifesting outside the world and the weather affecting mementos but for some reason not palaces.