ELI5: Explain Like I'm 5

André–Quillen cohomology

Okay kiddo, imagine you have a puzzle that is made up of many small pieces that fit together perfectly. Now, imagine there are different ways to put the puzzle together that can create new shapes or pictures.

In math, there are also many ways to fit pieces together, but instead of puzzle pieces, we call them "modules". These modules can be put together in different ways to create new shapes and structures.

André-Quillen cohomology is a way to study how these modules fit together and how they interact with each other. It helps us understand more about the shapes and structures that can be created from these modules.

Think of it like a detective trying to solve a mystery. The André-Quillen cohomology helps us piece together clues and understand how everything fits together to solve the puzzle.

It may sound complicated, but it's actually quite fun! Who knows, maybe one day you will be a math detective yourself!