Quasi-category

Okay, so imagine you have a bunch of toys - some are dolls, some are cars, some are stuffed animals, and so on. You want to put them all in different boxes so that the dolls are in one box, the cars in another, and so on.

Now, imagine you also have some toys that you're not quite sure where to put - they could go in more than one box. For example, you have a toy car that can also transform into a robot.

In mathematics, we have something called a "quasi-category" that helps us organize things like these toys. A quasi-category is like a bunch of boxes (called "simplices"), where we can put things (called "objects" or "points"). But unlike regular boxes, each object can belong to more than one box - kind of like how our toy car belongs to both the car and robot boxes.

To keep track of which objects belong to which boxes in our quasi-category, we use something called "morphisms" - these are like arrows that show us how to move from one object to another. For example, if we have a morphism from the toy car to the car and another from the toy car to the robot, we know that the toy car belongs in both of those boxes.

Overall, a quasi-category is a way of organizing things that can be in multiple places at once, and it helps mathematicians study some really complex and interesting concepts.