Bewildered of Cambridge writes …

A few posts back, I quoted Tom Leinster: “The level of abstraction in the Yoneda Lemma means that many people find it quite bewildering.” I can relate to that. Just a couple of days ago I managed to bewilder myself for a long afternoon, and it took me an embarrassing amount of time to locate where I’d composed arrows the wrong way around (contravariance bites back). I have a rule when writing this sort of expository stuff not to look things up, on the principle that working things out again for myself from first principles much increases the chances of being able to explain the topic lucidly to others. But the rule has its downside sometimes!

Anyway …

There is now a fifteen page chapter on Yoneda (the theorem, not its implications which I plan to tackle next). I take things in three stages, proving what I (non-standardly) call the Restricted Yoneda Lemma, and then the Intermediate Yoneda Lemma, before getting to the fully caffeinated Yoneda Lemma. The hope is that, chunked up like this,  each of the three stages almost writes itself …

For enthusiasts, the latest version of Category Theory II is here.

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