It looks like you're new here. If you want to get involved, click one of these buttons!

- All Categories 2.2K
- Programming with Categories Course 24
- Exercises - Programming with Categories Course 15
- Mini-Talks - Programming with Categories Course 3
- Applied Category Theory Course 341
- Applied Category Theory Seminar 4
- Exercises - Applied Category Theory Course 149
- Discussion Groups 50
- How to Use MathJax 15
- Chat 487
- Azimuth Code Project 108
- News and Information 147
- Azimuth Blog 149
- Azimuth Forum 29
- Azimuth Project 189
- - Strategy 108
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 711
- - Latest Changes 701
- - - Action 14
- - - Biodiversity 8
- - - Books 2
- - - Carbon 9
- - - Computational methods 38
- - - Climate 53
- - - Earth science 23
- - - Ecology 43
- - - Energy 29
- - - Experiments 30
- - - Geoengineering 0
- - - Mathematical methods 69
- - - Meta 9
- - - Methodology 16
- - - Natural resources 7
- - - Oceans 4
- - - Organizations 34
- - - People 6
- - - Publishing 4
- - - Reports 3
- - - Software 21
- - - Statistical methods 2
- - - Sustainability 4
- - - Things to do 2
- - - Visualisation 1
- General 41

Options

## 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!`