The following confuses me:

Data:

db.foo.insert({name: "Hello"})

Operation:

db.foo.aggregate({$project: { "_id": 0, "Hello" : {$map: {input: ["$name"],  as: "whee", in: "$$whee"} } }})

Result:

{ "Hello" : [ "$name" ] }

Somehow I would have expected $name to be expanded to "Hello".
I'm sure there's a good reason that doesn't happen, but I couldn't find anything on the site that explains exactly what's going on here