8 Crazy Pixar Fan Theories
4. Andy's Monster
From a Jessie doll appearing in Boo's bedroom, to Claws opening a door and being scared by a child almost touching him (with a poster appearing there and in Sid's bedroom), there's a strong suggestion Toy Story and Monsters Inc. coexist in one world.
On that basis it stands to reason that Andy, as a child, would have a monster whose job it is to scare him. Of course, this would then require a door for the monster to travel through. We see Andy's bedroom door in Toy Story, but alas no such door appears amongst the countless ones seen in Monsters Inc. This doesn't rule anything out though, as it may just be a door we don't see, or as theory creator SuperCarlinBrothers notes, because he's no longer scared. Going instead to the Monsters University website, on a short video there, what appears to be Andy's door does make an appearance.
That just leaves the question of which monster is scaring Andy. And there's a spine-tingling answer to that. If we look at his bedroom he has a wallpaper that features a cloud pattern. Watch Monsters Inc., and we see one monster practicing his routine against a very similar background. Yes - Randall is Andy's monster.