Kan complex

Okay, kiddo, so imagine you have some toys that you really love to play with. Now, these toys are all different shapes and sizes, some are round, some are square, some are big and some are small.

Now, think of kan complex as a special way to sort and organize all these different toys based on their shapes and sizes. Just like how we might sort our toys into different piles depending on what they look like or how big they are, kan complex helps us sort mathematical objects into different categories depending on certain rules.

For example, if we have a bunch of shapes that are all rounded, we might put them into one pile called "round toys". Similarly, if we have a bunch of mathematical objects that all have certain properties, we can use kan complex to organize them into categories called "simplices".

So, kan complex is a really useful tool for mathematicians to help them study and understand different types of mathematical objects. Just like how we use different colors or shapes to help us sort and organize our toys, mathematicians use kan complex to help them sort and organize mathematical concepts!