The homework for the next meeting is to take notes on the chapters from the text on the Yoneda Embedding and the Yoneda Lemma.
We had a good and interesting meeting. At the end of it, @AndriusKulikauskas presented the graph on the Yoneda Lemma which he had posted a while back. Hashing it out there, my conjecture is that what he was getting at is an extension to the Yoneda Lemma, in which the bijection gets enriched to a natural isomorphism. This is stated for example in the language MacLane uses, "The Yoneda map is natural in K and r."
So our strategy will be to first study the Yoneda Lemma as it is stated, as such, in terms of a bijection. Then we will cover the extension to the lemma, and revisit Andrius' diagram.