Hi √Čricles,
Welcome to the forum! Presently there are only a few people active at this time, so, even though it is a good idea, it is possible that you may not get much response to this specific suggestion. Time will tell. In any case, feel free to post any study notes on the forum; I would be interested to read them. You could, for example, start a discussion called Notes on Lambek's Introduction to Higher Order Categorical Logic. That would give people an opportunity to comment or ask questions.