convert a $lookup result to an object instead of array

You can use $arrayElemAt in $project stage.

Syntax of $arrayElemAt is { $arrayElemAt: [ <array>, <idxexOfArray> ] }

like:

mongoose.model('Discipline').aggregate([
   {
      $match: {
        project: mongoose.Types.ObjectId(req.params.projectId)
      },
   },
   {
      $lookup: {
        from: "typecategories",
        localField: "typeCategory",
        foreignField: "_id",
        as: "typeCategory"
      }
   },
   {
      $project: {
         name: 1, typeCategory: {$arrayElemAt:["$typeCategory",0]}
      }
   }
]);

Use $first to return the first element in the array:

$project: {
    title: 1, 
    typeCategory: {$first: "$typeCategory"}
}

You can just use $unwind. It deconstructs an array field from the input documents to output a document for each element

let query = mongoose.model('Discipline').aggregate([
    {
      $match: {
        project: mongoose.Types.ObjectId(req.params.projectId)
      },
    },
    {
      $lookup: {
        from: "typecategories",
        localField: "typeCategory",
        foreignField: "_id",
        as: "typeCategory"
      }
    },
    {$unwind: '$typeCategory'},
    {
      $project: {
        title: 1, typeCategory: "$typeCategory"
      }
    }
  ]);