Presheaf of spaces

Imagine you have a big map of your town or city. Now, let's say each building or house in your town has a special marker or color on the map. This makes it easy to locate each building or house on the map.

In mathematics, we use a similar idea to describe how things are related to each other. A presheaf of spaces is like a map that tells you where different "spaces" are located and how they are related to each other.

A presheaf of spaces is made up of two things: a "space" (like a building or house on the map) and a rule that tells you how that space is related to other spaces nearby. For example, if you have a house, the rule might tell you which other houses are nearby or which streets it connects to.

This is really useful when you're trying to understand how different things in math are connected. It helps you find your way around and see where everything fits in. So just like a map helps you find your way around your town or city, a presheaf of spaces helps you find your way around math!