The timeline begins with Brave, set in the Dark Ages. It explains why animals can have human characteristics. Magic is provided by a witch, who mysteriously vanishes every time she goes through a door.
The animals affected interbreed, which explains why they can talk in other Pixar movies – ehem! Ratatouille, Bug’s life etc.
Up’s Charles Muntz creates technology to harness the animals’ power. But Dug, the dog, foils his plan, and the relationship between humans and animals worsens. The animals’ intelligence grows, which is proved in Finding Nemo. Resulting in an industrial revolution that begins in Up, run by the corporation Buy-N-Large (BNL).
BNL is also the reason that humans in Wall-E flee to space, proving that technology gains power over humans.
The Incredibles’ Syndrome uses this technology in attempts to create a genocide. Technology’s rise and the industrial revolution leads to pollution. Which makes Earth unfit for humans and that humans become dependent on machines – Wall E. But in the end credits of Wall-E, life returns to Earth, resulting in A Bug’s Life.
In the meantime, a new super species is born. – Monster’s inc.
The monsters have an energy crisis, which is supplied by the humans… by way of time travel. Each door is a time machine, and it’s the only way they come into contact with humans. That’s also how the monsters harvest energy. Boo now knows of a future world.
“She remembers that doors are the key to how she found Sully in the first place and becomes…”
Boo now becomes the witch from Brave.
She uses the will-of-the-wisps for time travel, which explains why she’s now in the Dark Ages. In other words, she magically creates these doors to find Sully.
And we know this because of the carving of Sully on her wood.
Source: Buzzfeed.com