Comma category
A comma category is a way of looking at how different things are related to each other. It's like when you play with your toys and put them in groups based on their similarities. For example, you might put all your toy cars together in one group and your stuffed animals in another group.
The comma category works in a similar way, but it's all about the relationships between objects that have arrows between them. Just like you might draw lines between your toys to show how they're related, mathematicians draw arrows between objects in a category to show how they're related.
Now, imagine you have three different toys - a car, a truck, and a ball - and you draw arrows between them based on how they're related. You might draw an arrow from the car to the truck because they're both vehicles, but you wouldn't draw an arrow from the ball to the car because they aren't related in the same way.
In a comma category, you take two categories and "stick" them together using a comma. For example, you might take the category of all vehicles (like cars and trucks) and stick it together with the category of all colors (like red and blue). The result is a new category that shows how vehicles and colors are related.
To be more specific, a comma category takes two categories and "pairs up" all the possible ways you can link them together using arrows. It's like making a big table where you list all the pairs of objects and how they're related based on the arrows you draw.
In summary, a comma category is a way of thinking about how things are related to each other. It's like grouping your toys based on similarities and drawing arrows between them to show how they're related. By using a comma to combine two categories, mathematicians can explore all the possible ways that objects in those categories can be related to each other.
The comma category works in a similar way, but it's all about the relationships between objects that have arrows between them. Just like you might draw lines between your toys to show how they're related, mathematicians draw arrows between objects in a category to show how they're related.
Now, imagine you have three different toys - a car, a truck, and a ball - and you draw arrows between them based on how they're related. You might draw an arrow from the car to the truck because they're both vehicles, but you wouldn't draw an arrow from the ball to the car because they aren't related in the same way.
In a comma category, you take two categories and "stick" them together using a comma. For example, you might take the category of all vehicles (like cars and trucks) and stick it together with the category of all colors (like red and blue). The result is a new category that shows how vehicles and colors are related.
To be more specific, a comma category takes two categories and "pairs up" all the possible ways you can link them together using arrows. It's like making a big table where you list all the pairs of objects and how they're related based on the arrows you draw.
In summary, a comma category is a way of thinking about how things are related to each other. It's like grouping your toys based on similarities and drawing arrows between them to show how they're related. By using a comma to combine two categories, mathematicians can explore all the possible ways that objects in those categories can be related to each other.