Equivariant bundle

Imagine a big box of toys that has some special rules. Normally, when you move the box around, the toys inside move with it. But sometimes, there are certain toys that always stay in the same place no matter where you move the box. These special toys are called "equivariant" toys.

Now imagine that instead of toys, we have different things called "bundles" inside the box. These bundles are kind of like special bags that hold other things. Just like with the toys, we can move the box around and the bundles inside will move too, unless they are equivariant.

An "equivariant bundle" is a special kind of bundle where certain parts of it are equivariant. This means that even if we move the box around, those parts of the bundle will stay in the same place relative to the box.

So imagine we have a ball inside an equivariant bundle. If that ball is equivariant, it will always stay in the same spot inside the bundle no matter how we move the box around. But if the ball is not equivariant, it will move around inside the bundle with the rest of the bundle when we move the box around.

Overall, an equivariant bundle is just a fancy name for a bundle with some special parts that stay in the same place when you move the box around.