Given the following collection

db.playground.insertMany([
  { "id": 1, "tags": [{"t": "T1", "v": "t11", "c": 1 }, {"t": "T2", "v": "t12"}, {"t": "T3", "v": "t13"}]},
  { "id": 2, "tags": [{"t": "T1", "v": "t21", "c": 2 }, {"t": "T2", "v": "t22"}, {"t": "T3", "v": "t23"}]},
  { "id": 3, "tags": [{"t": "T1", "v": "t22", "c": 2 }, {"t": "T2", "v": "t21"}, {"t": "T3", "v": "t33"}]},
])

How could I filter the tags array for each document so that they only contain:

• The tags with t = T2 or t = T3 if there’s at least one tag in the same array with t = T1, v = t21 and c = 1
• The tags with t = T1 or t = T3 if there’s at least one tag in the same array with t = T1, v = t21 and c = 2

This is my current attempt at it, but there are some issues with it:

1. I don’t understand why the predicate { $eq: ["$tags.v", "t21"] } doesn’t work
2. I don’t understand why this requires square brackets { $eq: ["$tags.c", [1]]} and it doesn’t work when I use NumberInt like here { $eq: ["$tags.c", NumberInt(1)] }
3. How can I make sure that c and v belong to the same tag, my current example also returns the 3rd entry which meets one condition on one tag and the second on the other.

db.playground.find({},
  {
    id: 1,
    tags: {
      $filter: {
        input: "$tags",
        as: "tag",
        cond: {
          $or: [
            { $and: [
                // { $eq: ["$tags.v", "t21"]}, // Why does this not work
                { $eq: ["$tags.c", [1]]}, // Why does this work as an array?
                { $in: ["$$tag.t", ["T2", "T3"]] }
              ]
            },
            { $and: [
                // { $eq: ["$tags.v", "t21"]}, // Why does this not work
                { $eq: ["$tags.c", [2]]},  // Why does this work as an array?
                { $in: ["$$tag.t", ["T1", "T3"]] }
              ]
            }
          ]
        }
      }
  }}
)

Playground