Coherent sheaf
Okay kiddo, imagine you have a basket full of different fruits like apples, bananas, and oranges. Now, let's imagine that each fruit represents a mathematical concept called a "module".
Now, a "sheaf" is like a basket of those fruit-modules, but with some extra rules. We can only put certain fruits together in the basket if they are "compatible" with each other. For example, we definitely wouldn't put a watermelon in the basket with all those other small fruits.
A "coherent sheaf" is a type of basket that has a special rule. All of the fruits in the basket have to be able to be made from each other using certain rules, just like how you can turn apples into applesauce, apple juice, or apple pie. This means that we can take any fruit out of the basket and still make sense of what's left.
So, just like how we only put certain fruits together in a regular sheaf, a coherent sheaf only keeps together compatible fruit-modules that can be changed into each other in a certain way. That's it for coherent sheaves, little one!
Now, a "sheaf" is like a basket of those fruit-modules, but with some extra rules. We can only put certain fruits together in the basket if they are "compatible" with each other. For example, we definitely wouldn't put a watermelon in the basket with all those other small fruits.
A "coherent sheaf" is a type of basket that has a special rule. All of the fruits in the basket have to be able to be made from each other using certain rules, just like how you can turn apples into applesauce, apple juice, or apple pie. This means that we can take any fruit out of the basket and still make sense of what's left.
So, just like how we only put certain fruits together in a regular sheaf, a coherent sheaf only keeps together compatible fruit-modules that can be changed into each other in a certain way. That's it for coherent sheaves, little one!