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!
Comment Source: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!
Comments
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 quite as 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!