Localization of a category

Localization of a category means that we take a group of things (called a category) and make them smaller by only keeping the parts that we really care about. It's like picking out our favorite toys from a big toy box.

But how do we decide which parts to keep? Well, sometimes we only care about certain things in the category, like a specific shape or color. So we can make a new category that only has those things in it.

But wait, there's more! Sometimes there are things in the original category that are not exactly the same as each other, but are really close. So we can group them together in the new category and treat them as if they are the same thing.

Overall, localization of a category is a way of making things simpler and easier to understand by only focusing on the parts that matter the most.