| After having recalled the basic definitions, we present two algorithms, reciprocical to each other, that give the wanted bijection. |
| Removal of all references to partial bijection. |
| Two general facts: First, the structure map of an initial algebra on Set is always a bijection. |
| There is a bijection between every pair of equivalence classes: the inverse of a representative of the first equivalence class, composed with a representative of the second. |
| Note in particular that a function is a bijection if and only if it's both an injection and a surjection. |
| In fact, it is easy to see that this bijection provides a conjugacy. |
