Quotient space of an algebraic stack
Okay, kiddo, so let's talk about algebraic stacks first. An algebraic stack is like a big puzzle made up of smaller puzzle pieces, or objects in math that we call sheaves. These sheaves are kind of like groups of things that we put together.
Now, a quotient space of an algebraic stack is like taking that puzzle and squishing it down into a smaller puzzle with fewer objects. We do this by picking out certain objects in the puzzle and saying they are now the same thing. This makes things a little simpler and easier to understand.
Think of it like this: if you have a bunch of toy cars, some of them might be the same color or the same kind of car. So you might decide to put all the red cars together and call them "the red group" or put all the race cars together and call them "the race car group." That's kind of like what a quotient space does - it takes a big group of objects and puts some of them together to make a smaller group.
In math, we do this using something called an equivalence relation. This is like a rule that says some of the objects in our puzzle are the same thing. Once we have this rule, we can use it to "collapse" some of the objects together and make a new, simpler puzzle.
So, in summary, a quotient space of an algebraic stack is like taking a big puzzle made up of smaller pieces and squishing it down into a smaller puzzle by picking out certain objects and saying they are now the same thing. We use an equivalence relation to do this, which is like a rule that tells us which objects are "equivalent" in some way. Hope that helps, kiddo!
Now, a quotient space of an algebraic stack is like taking that puzzle and squishing it down into a smaller puzzle with fewer objects. We do this by picking out certain objects in the puzzle and saying they are now the same thing. This makes things a little simpler and easier to understand.
Think of it like this: if you have a bunch of toy cars, some of them might be the same color or the same kind of car. So you might decide to put all the red cars together and call them "the red group" or put all the race cars together and call them "the race car group." That's kind of like what a quotient space does - it takes a big group of objects and puts some of them together to make a smaller group.
In math, we do this using something called an equivalence relation. This is like a rule that says some of the objects in our puzzle are the same thing. Once we have this rule, we can use it to "collapse" some of the objects together and make a new, simpler puzzle.
So, in summary, a quotient space of an algebraic stack is like taking a big puzzle made up of smaller pieces and squishing it down into a smaller puzzle by picking out certain objects and saying they are now the same thing. We use an equivalence relation to do this, which is like a rule that tells us which objects are "equivalent" in some way. Hope that helps, kiddo!