A have several questions regarding this example (it refers to Proposition 6.3.7 from here):
First, regarding "... whereas a least element is an empty join." In the proof of Proposition 6.3.7 (see the link above), to prove that $(A\implies G)$ has a least element, Leinster took the meet to be a least element. And it makes sense, since by definition, a meet of a set is (in particular) less than or equal to everything else in the set. Isn't this exactly the definition of a least element? So in the proof, the meet was used as a least element, but in Example 6.3.8 it's kind of alluded to the fact that a least element is not a meet, but a join. Or is it not claimed that a least element is not a meet in Example 6.3.8? But then why is "join" italicized?
And second, how does it follow from (6.19) [see "Proposition 6.3.7" above] that the least element of $B$ is $\land B$? I don't see this at all.
Edit: I've also realized that I don't quite understand how exactly (6.19) [see the link "Proposition 6.3.7" above] follows from Corollary 2.3.7. If someone could explain it, that'd be great, too.
