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At co-Yoneda lemma I have tried to harmonize the notation and polish the formatting a little. For instance, earlier the statement had been in terms of $V$-enrichment, but then the proof was stated in terms of $Set$-enrichment, I have harmonized that.
Then I added as an Example an elementary proof of the co-Yoneda lemma in $Set$ in terms of inspecting the defining coequalizer as a set of equivalence classes of pairs.
For what it’s worth, this claim looks incorrect:
In this MO answer, Tom Leinster referred to the co-Yoneda lemma as ninja Yoneda lemma
On the contrary, he says that “ninja category theorists” would call it just the plain “Yoneda lemma”.
I think jokes enshrined in mathematical terminology get old quickly and then stay old forever. I vote for not promoting this.
I think jokes enshrined in mathematical terminology get old quickly and then stay old forever. I vote for not promoting this.
I completely agree.
I took the liberty of deleting the “ninja”-section.
Because, first, it’s claim that “Tom Leinster referred to the co-Yoneda lemma as ninja Yoneda lemma” was just false, and second its mathematical content was a direct repetition of the material in this entry.
(There may be room to state this material more clearly/concisely, but repeating it as if it were a different statement is confusing.)
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