Ext functor

An Ext functor is a way for our math friends to measure how different two things are. Let's pretend we have two groups, or math friends, called A and B. The Ext functor helps us measure how different A and B are by looking at how similar or different their "exterior" behavior is.

To figure out how similar or different A and B are, we take their exterior behavior, that is, the way they interact with other groups, and compare them. This is like comparing two kids in a playground to see how different they are. If they both like playing with toys but one kid likes cars and the other kid likes dolls, we know they are different.

In the same way, the Ext functor compares how A and B behave when they interact with other groups, just like comparing how the playground kids behave when playing with toys. If A and B behave very differently when they interact with other groups, they have a high Ext value, but if they behave similarly, they have a low Ext value.

So, when math friends want to figure out how different two groups are, they use the Ext functor to measure their exterior behavior and determine if they are similar or different.