Chapter 1, page 2:

One might call these surprised {\it generative effects}.

Should be:

One might call these surprises {\it generative effects}.

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page 5:

A ≤ B in the poset if

seems to be a grammatical whoopsie.

Also, poset'' hasn't been defined at this point, which I suspect is not what the authors wanted, with this being a math book and all, although personally I rather like words being used before they're defined.

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The existence of the generative effect,
however, is captured in the inequality
Φ(A) ∨ Φ(B) ≤ Φ(A ∨ B).
(1.3)
This can be a strict inequality ...

If I understand correctly, the formula only captures a generative effect if it IS a strict inequality (not just can be one).

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page 5 again:

the map Φ preserves some structure but not others

should be:

the map Φ preserves some structures but not others