Exotic Matter Laboratory
Purple key
Goes in the cargo elevator console, next to the green key.
What it is for
Where the walkthrough uses it
3-2 The Assembly Line· step 2both players
Get the two keys. The Goop Gun player climbs to the purple-carpet office (a goop stair onto the grey block, then a blob on its pressure plate folds the plank down) and hangs on the monkey bars there. Bar 1 opens the green key's hatch: the Hook Gun player hooks the key from the gallery up the stairs behind the fuse door. Bar 2 opens the green shutter in the hall: the Hook Gun player pulls out the push block, climbs into the channel and hooks the purple key through a low gap.
3-2 The Assembly Line· step 3both players
Put both keys in the cargo lift's console.
Where to find it
No item spot is random: the game files place every item in the same spot in every game. Some items exist several times at once, such as the fuses in the Time Maze. From the game files: the area is loaded at these checkpoints. A door on the way can still be locked at some of them.
How to find it
At the end of the narrow conveyor in the dark chute, under a vent grate, about 3 m above the floor.
Checkpoints where its area is loaded
- 3-2 The Assembly Line · both players
5 mSeen from above with the ceiling removed. Yellow ring: this spot. Small labels: other spots of the same item close by (select one to go to it). 
The spot seen from nearby (rendered from the game's own level geometry).
Achievements
Onwards and Upwards
Activated the Cargo Elevator
How it unlocks (spoiler)
Both of you stand on the cargo elevator (3-2 The Assembly Line), then pull its chain all the way.
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