Factorization homology
Okay kiddo, so factorization homology is like when you have a bunch of shapes (let's call them "spaces") and you want to figure out how they fit together in different ways.
For example, imagine you have a square and a triangle. When you put them together, they make a bigger shape that looks kind of like a house. But, you could also take the triangle and put it on top of the square to make a different shape, like a hat.
Now, let's say each space has something inside of it. Maybe the square has a green block and the triangle has a blue ball. So, when you put them together to make the house shape, there's a green block and a blue ball inside. But, if you put them together to make the hat shape, the green block is still there but the blue ball isn't there anymore.
Factorization homology is like figuring out all the different ways you can put the spaces together and what happens to the things inside them when you do. It's a way to study how different shapes interact with each other and how that affects what's inside of them.
In more grown-up terms, factorization homology is a mathematical tool that looks at how algebraic structures (like groups or rings) change when you move them around different spaces. It's useful for studying things like topological field theories and quantum mechanics. But, the basic idea is still the same - figuring out how things fit together in different ways and how that affects what's inside them.
For example, imagine you have a square and a triangle. When you put them together, they make a bigger shape that looks kind of like a house. But, you could also take the triangle and put it on top of the square to make a different shape, like a hat.
Now, let's say each space has something inside of it. Maybe the square has a green block and the triangle has a blue ball. So, when you put them together to make the house shape, there's a green block and a blue ball inside. But, if you put them together to make the hat shape, the green block is still there but the blue ball isn't there anymore.
Factorization homology is like figuring out all the different ways you can put the spaces together and what happens to the things inside them when you do. It's a way to study how different shapes interact with each other and how that affects what's inside of them.
In more grown-up terms, factorization homology is a mathematical tool that looks at how algebraic structures (like groups or rings) change when you move them around different spaces. It's useful for studying things like topological field theories and quantum mechanics. But, the basic idea is still the same - figuring out how things fit together in different ways and how that affects what's inside them.