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## Comments

`![picture](https://i.imgur.com/4kDBMhM.png)`

In your post on the 4-hop fixed point, you say:

The three-hop equivalence can be expressed this way too: \(f \circ g \circ f \cong f\) and \(g \circ f \circ g \cong g\). It's not

quiteas pretty, but it's there!`In your post on the [4-hop fixed point](https://forum.azimuthproject.org/discussion/2189/petepics-chapter-1-iterated-galois-maps-the-4-hop-fixed-point), you say: > Since these are true at every point, they can be expressed as statements about maps rather than about values The three-hop equivalence can be expressed this way too: \\(f \circ g \circ f \cong f\\) and \\(g \circ f \circ g \cong g\\). It's not _quite_ as pretty, but it's there!`