Projective object
Okay kiddo, let's talk about projective objects. Imagine you have a toy car and you want to take a picture of it. You could hold the camera straight on and take a picture, but then you might miss some of the cool details on the car, like the wheels or the spoiler. So instead, you might tilt the camera a little bit and take a picture from a different angle. This makes the car look different in the picture, but it still represents the car in some way.
Now, imagine that instead of a toy car, we have an object in math. We want to take pictures (or "maps") of this object using other objects in math. A projective object is kind of like that toy car - it's an object that can be represented in different ways by different "maps" from other objects. This means that even if the "maps" look different, they still somehow represent the same thing.
Let's use an example. Imagine we have an object called a "point" in math. We can take a picture of this point by using a line, and drawing a line from the point out to infinity. This is called a "projective map" because it takes the point and turns it into a line. But we could also take a different kind of projective map, where we take two different points and draw a line between them. This represents the relationship between those two points, but it still somehow represents the original point, because we know that any two distinct points determine a unique line which goes through both of them.
So, a projective object is kind of like a toy car that can be represented in different ways, and projective maps are like different pictures we can take of the car from different angles. Even if the pictures look different, they still somehow show the same thing - just like projective maps show the same underlying object even though they may look different.
Now, imagine that instead of a toy car, we have an object in math. We want to take pictures (or "maps") of this object using other objects in math. A projective object is kind of like that toy car - it's an object that can be represented in different ways by different "maps" from other objects. This means that even if the "maps" look different, they still somehow represent the same thing.
Let's use an example. Imagine we have an object called a "point" in math. We can take a picture of this point by using a line, and drawing a line from the point out to infinity. This is called a "projective map" because it takes the point and turns it into a line. But we could also take a different kind of projective map, where we take two different points and draw a line between them. This represents the relationship between those two points, but it still somehow represents the original point, because we know that any two distinct points determine a unique line which goes through both of them.
So, a projective object is kind of like a toy car that can be represented in different ways, and projective maps are like different pictures we can take of the car from different angles. Even if the pictures look different, they still somehow show the same thing - just like projective maps show the same underlying object even though they may look different.