Greetings, 

I know that if having a field named "info", to set the default value of that field i will have to add context like this

{'default_info':'info_value'}

such that when a user tries to create a product, there is a default parent category selected.

Just thinking, does this which does not work make sense? 

{'default_product_tmpl_id.categ_id.parent_id.name':'product_parent_name'}