Optimal way to model documents hierarchy in CouchDB

I'm trying to model document a hierarchy in CouchDB to use in my system, which is conceptually similar to a blog. Each blog post belongs to at least one category and each category can have many posts. Categories are hierarchical, meaning that if a post belongs to CatB in the hierarchy "CatA->CatB" ("CatB is in CatA)", it belongs also to CatA.

Users must be able to quickly find all post in a category (and all its children).

Solution 1 Each document of the post type contains a "category" array representing its position in the hierarchy (see 2).

{
   "_id": "8e7a440862347a22f4a1b2ca7f000e83",
   "type": "post",
   "author": "dexter",
   "title": "Hello",
   "category":["OO","Programming","C++"]
}

Solution 2 Each document of the post type contains the "category" string representing its path in the hierarchy (see 4).

{
   "_id": "8e7a440862347a22f4a1b2ca7f000e83",
   "type": "post",
   "author": "dexter",
   "title": "Hello",
   "category": "OO/Programming/C++"
}

Solution 3 Each document of the post type contains its parent "category" id representing its path in the hierarchy (see 3). A hierarchical category structure is built through linked "category" document types.

{
   "_id": "8e7a440862347a22f4a1b2ca7f000e83",
   "type": "post",
   "author": "dexter",
   "title": "Hello",
   "category_id": "3"
}

{
   "_id": "1",
   "type": "category",
   "name": "OO"
}


{
   "_id": "2",
   "type": "category"