I am reading the book MongoDB in Action. I have a question about Chapter 4: Document-oriented data.
On Page 58, the book gives an example for many-to-many relations. It gives Product document and Category document.
Product


Category

My question
I understand the many-to-many association here. Basically, Product can have a key with array of Category _id, etc. So I am not trying to ask a question like this MongoDB Many-to-Many Association
My question is about Page 61, where the book gives two example queries about querying the many-to-many relations. Here is the two queries:

What does
=>mean? I thought=>only exists in Ruby driver usage.What is the
categoryincategory['_id']? Is it a collection?What is the
productinproduct['category_ids']?How is the first query related to
Gardening Tools categoryas described above the first query?
The book doesn't explain these two queries in details.
Can someone explain more about querying for many-to-many?