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I started to read Lambek & Scott's work. Is here anyone who versed in it and could answer my questions privately, in some light supervision way, discussing research ideas?
Of course it's up to you, but if you ask questions publicly more people will be motivated to answer them, more people will learn from the answers, and we'll get interesting conversations about these ideas. Indeed one of the main points of this Zulip is to answer and discuss questions - especially at #learning: questions.