definitions and proofs
If your mathematical objects are defined recursively, then the proofs involving them will inevitably contain inductive methods. Similarly, if they are defined via universal properties, the proofs will be built on categorical techniques.
This allows us to make a simple but an important observation: The nature of the objects determines what you can do with them. That is why recasting the original structure in a different fashion can lead to new insights.
This allows us to make a simple but an important observation: The nature of the objects determines what you can do with them. That is why recasting the original structure in a different fashion can lead to new insights.
