Proper morphism

A proper morphism can be thought of as a rule that turns one kind of thing into another kind of thing, but all the rules have to follow specific guidelines to be called "proper." Imagine you have a bunch of toy cars and you want to turn them into toy trucks. If you follow the proper rules, you will end up with a toy truck that looks like it's supposed to and works the way it's supposed to.

In math, we have rules that must be followed when we transform one mathematical object into another. A proper morphism is a specific rule that must be followed to make sure the transformation is done correctly. Just like with toy cars and trucks, there are certain things we need to pay attention to when we make this transformation. For example, we need to make sure the shape, size, and properties of the original mathematical object are preserved when we turn it into the new object.

A proper morphism is important because we want to be sure that the things we transform follow specific rules and don't turn out weird or unusable. It's like playing a game where everyone has to follow the rules in order for the game to be fun and fair. Proper morphisms make sure that the math we do is fun and fair, too!