Thin category
Well kiddo, imagine you have a bunch of different things in a group, like different types of fruit. Some fruits are very similar to each other, like apples and pears, while others are very different, like bananas and strawberries. A thin category is a group where all the things in it are very similar to each other and there are not many differences between them.
For example, imagine a category of animals that only includes dogs. All dogs are pretty similar, they have fur, four legs, bark or growl, and are frequently pets. There's not a lot of diversity within the category of dogs. On the other hand, a category of animals that includes dogs, cats, birds, and fish is a thick category because these animals are very different from each other.
In math, people use the idea of a thin category to talk about groups of things that are very similar to each other, like groups of numbers or shapes. It helps mathematicians study these things in more detail and understand how they relate to each other.
For example, imagine a category of animals that only includes dogs. All dogs are pretty similar, they have fur, four legs, bark or growl, and are frequently pets. There's not a lot of diversity within the category of dogs. On the other hand, a category of animals that includes dogs, cats, birds, and fish is a thick category because these animals are very different from each other.
In math, people use the idea of a thin category to talk about groups of things that are very similar to each other, like groups of numbers or shapes. It helps mathematicians study these things in more detail and understand how they relate to each other.