$addFields is not adding value in document - mongodb

Question

Query is as follows and result is given below:
What I want is I am adding field called name, in which I want categoryObj[0].categoryName but it is empty.
Tried categoryObj.$.categoryName but giving error.
Once name is obtained as I want i will exclude categoryObj with project opertator.
Thanks for help in advance
let itemsByCategory = await VendorItem.aggregate([
{$match: {vendor: vendorId}},
{$lookup: {
from: "vendorcategories",
localField: "category",
foreignField: "_id",
as: 'categoryDetails'
}},
{$group:{
"_id":"$category",
"count":{"$sum":1},
"items":{"$push":"$$ROOT"},
"categoryObj":{"$addToSet":"$categoryDetails"}
}},
{$project: {"items.categoryDetails":0}},
{$addFields: {"categoryName" : "$categoryObj.categoryName"}},
//{$project: {"categoryObj":0}},
]);
and the result is as follows
{
"itemsByCategory": [
{
"_id": "62296d612a1462a7d5e4b86b",
"count": 1,
"menuItems": [
{
"_id": "622971fa4fda7b4c792a7812",
"category": "62296d612a1462a7d5e4b86b",
"vendor": "62296c6f2a1462a7d5e4b863",
"item": "Dahi Chaat",
"price": 30,
"inStock": true,
"variants": [
{
"variantName": "With Sev",
"variantPrice": 40,
"_id": "622975b9f7bdf6c2a3b7703c"
}
],
"toppings": [
{
"name": "cheese",
"price": 10,
"inStock": true,
"_id": "62297766ff9f01d236c60736"
}
],
"categoryDetails": [
{
"_id": "62296d612a1462a7d5e4b86b",
"categoryName": "Snacks",
"categoryDescription": "Desciption changed!",
"vendor": "621c6c944d6d79e83219e59a",
"__v": 0
}
]
}
],
"categoryObj": [
[
{
"_id": "62296d612a1462a7d5e4b86b",
"categoryName": "Snacks",
"categoryDescription": "Desciption changed!",
"vendor": "621c6c944d6d79e83219e59a",
"__v": 0
}
]
],
"name": []
}
]
}

Answer 1

You can add an $unwind phase in order to "loop" all objects inside "categoryObj", but you will need to group it back afterwards:
{"$addFields": {orig_id: "$_id"}},
{"$unwind": "$categoryObj"},
{"$addFields": {"name": {"$arrayElemAt": ["$categoryObj", 0]}}},
{"$group": {_id: "$orig_id", name: {$push: "$name.categoryName"},
menuItems: {$first: "$menuItems"}, count: {$first: "count"},
}
}
See playground here:
https://mongoplayground.net/p/wsH2Y0UZ_FH