Univalence axiom

The univalence axiom is a big, grown-up math idea that helps us talk about different types of things that are the same. Imagine you have a toy car and a toy truck – they are different, but they have something in common: they are both toy vehicles.

In math, we have different types of things too, like sets of numbers or shapes. And sometimes, two different types of things can be considered the same in a special way. Just like how the toy car and toy truck are both toy vehicles.

The univalence axiom helps us say that if two different types of things are the same in this special way, then we can use them interchangeably. It’s like if you had a toy car and a toy truck that were exactly the same size and could fit in the same toy garage. You could use either one to play with in the garage.

But not everyone agrees on whether the univalence axiom is a good idea or not – some math experts think it’s really useful, while others think it’s not necessary. So, it’s an ongoing debate in the math world.