Cohomology of categories
So, imagine you have a bunch of toys - some are similar to each other and some are different. And you want to study them to see how they are connected to each other.
Now, imagine that each of these toys is like a category - it has some objects (like the different parts of the toy) and some arrows between them (like how the parts fit together).
Cohomology of categories is a way to understand how these categories (or toys) are connected to each other. We can do this by looking at certain properties of the categories and their arrows.
For example, we might want to know if there are any "holes" in the category - this means there are objects that cannot be reached from others through the arrows. Or we might want to see how "twisted" the arrows are - this means they don't follow a straight path but instead go around in circles.
Cohomology of categories helps us understand these properties by using something called a "complex." This is a fancy word for a bunch of objects and arrows that are connected to each other.
We can then use some math magic to "measure" the complex and find out its cohomology. This is kind of like measuring how big a toy is or how heavy it is.
Overall, cohomology of categories is a way to study the connections between different toys (or categories) by looking at their properties and measuring them with math.
Now, imagine that each of these toys is like a category - it has some objects (like the different parts of the toy) and some arrows between them (like how the parts fit together).
Cohomology of categories is a way to understand how these categories (or toys) are connected to each other. We can do this by looking at certain properties of the categories and their arrows.
For example, we might want to know if there are any "holes" in the category - this means there are objects that cannot be reached from others through the arrows. Or we might want to see how "twisted" the arrows are - this means they don't follow a straight path but instead go around in circles.
Cohomology of categories helps us understand these properties by using something called a "complex." This is a fancy word for a bunch of objects and arrows that are connected to each other.
We can then use some math magic to "measure" the complex and find out its cohomology. This is kind of like measuring how big a toy is or how heavy it is.
Overall, cohomology of categories is a way to study the connections between different toys (or categories) by looking at their properties and measuring them with math.