Not at all clear, since you didn't describe your table structure nor show your working SQL query. But guessing based on the names, all you need is something like this:
IEnumerable<CategoryModel> CategoryList =
from procat in this.objDB.tbl_category
join product in this.objDB.tbl_Product on procat.cat_id equals product.pro_fk_cat_id into productdetail
from productdetaildata in productdetail.DefaultIfEmpty()
select new CategoryModel
{
cat_name = procat.cat_name,
cat_id = procat.cat_id,
related_count = productdetaildata.Count()
};