Match on subdocument key in aggregation pipeline

Given that I have a hash subdocument within my document, how can I match a value - categoryId (itself added using $addFields) - to the sub-document key - categoryTypes - in my aggregation pipeline:
ex:

{
   _id: $someId,
   categoryId: 2,
   categoryTypes: {
     1: "hello world",
     2: "something else",
     3: "still more stuff"
   }
}

I need to match categoryId (2) to key in categoryTypes (2). In essence I need to say:

$match: { categoryId: categoryTypes }

Thanks!

One option is to use $objectToArray:

db.collection.aggregate([
  {$set: {allKeys: {$objectToArray: "$categoryTypes"}}},
  {$match: {$expr: {$in: [{$toString: "$categoryId"}, "$allKeys.k"]}}},
  {$unset: "allKeys"}
])

See how it works on the playground example

Well it turns out that's simpler than I originally thought:

1- First changed the hash into an array which produced a subdocument which looks like ARRAY: [ "0": {...}, "1": {...}, ...]

// this is happening in $addFields stage
categories: { "$objectToArray": "$categoryTypes"}

2- Then in my project stage I did:

category: {
    $filter: {
        input: '$categories',
        as: 'item',
        cond: {$eq: ['$$item.k', "$categoryId"]}
    }}

Hope this helps others who may be looking for a similar solution.