Mongodb aggregation lookup with conditions

First of all, it is all_category_id, not category_id. Secondly, you don’t link articles – all documents will have exactly the same article_category array. Lastly, you probably want to filter out articles that don’t have matched category. The conditional pipeline should look more like this:

db.article.aggregate([
  { $match: {
      title: { $regex: /example/ }
  } },
  { $lookup: {
    from: "article_category",
    let: {
      article_id: "$article_id"
    },
    pipeline: [
      { $match: {
          $expr: { $and: [
              { $in: [ 8, "$all_category_id" ] },
              { $eq: [ "$article_id", "$$article_id" ] }
          ] }
      } }
    ],
    as: "article_category"
  } },
  { $match: {
    $expr: { $gt: [
      { $size: "$article_category"},
      0
    ] }
  } }
] )

UPDATE:

If you don’t match article_id, the $lookup will result with identical article_category array to all articles.

Let’s say your article_category collection has another document:

{
  "article_id": 0,
  "all_category_id": [5,8,10]
}

With { $eq: [ "$article_id", "$$article_id" ] } in the pipeline the resulting article_category is

[ 
  { 
    "article_id" : 2015110920343902, 
    "all_category_id" : [ 5, 8, 10 ] 
  } 
]

without:

[ 
  { 
    "article_id" : 2015110920343902, 
    "all_category_id" : [ 5, 8, 10 ] 
  },
  {
    "article_id": 0,
    "all_category_id": [ 5, 8, 10 ]
  }
]

If the later is what you need, it would be way simpler to make to find requests:

db.article.find({ title: { $regex: /example/ } })

and

db.article_category.find({ all_category_id: 8 })