- Analyze the twelvefold way, compare it with the twelve topologies, and consider what it may say about the kinds of equivalence relations possible.
- Is a set simply an equivalence class, in some sense? For example, the set is unordered but everything is labeled so that it could be ordered.
- In the usual foundation of combinatorial objects, we need to "label" and then "unlabel" (create an equivalence class). What is going on here? Is it possibly a lie?
- In the identity morphism, is there a difference between the "from" end and the "to" end?
Readings
Ideas
- Category theory - Categories are helpful in making fruitful definitions
- From dream: vectors A-B, B-A, consider the difference between them, the equivalence of A and B.
- Equations are questions.
- Isomorphism is based on assignment but that depends on equality up to identity whereas properties define establish an object up to isomorphism
- Symbols (a and b) are equal if they refer to the same referents. But equality has different meaning for symbols, indexes, icons and things. Consider the four relations between level and metalevel.
- Information can illustrate the different kinds of equivalences. Like returning a library book, a copy or a similar book.
- Identity morphisms allow us to define isomorphisms.