Strongly ribbon category
Okay kiddo, have you ever played with a ribbon before? It's a long piece of fabric that you can fold, twist, and tie into all sorts of shapes, right? Well, imagine that instead of playing with just one ribbon, we have a whole bunch of them!
In a strongly ribbon category, we have a bunch of ribbons - but they're not just regular ribbons. They have something special about them called "braiding." That means that we can twist and cross the ribbons over each other in certain ways, and it won't mess up the overall shape of the ribbons.
Now, let's say we want to do some math with these braided ribbons. We can take different ribbons, twist them together, and get new ribbons! And just like with the regular ribbons, we can tie them in all sorts of knots and shapes.
But here's where it gets a bit more complicated. We don't just want to play with the ribbons themselves - we also want to think about how they interact with each other. For example, if we have two ribbons that are twisted together, and we want to untwist them, how can we do that? There are certain rules we follow, like making sure we don't accidentally tie any new knots in the ribbons.
A strongly ribbon category is a special kind of math set where we can do all of this twisting, braiding, and unbraiding with the ribbons. And because we have all of these rules to follow, we can be sure that we're doing the math correctly and getting the right answers!
In a strongly ribbon category, we have a bunch of ribbons - but they're not just regular ribbons. They have something special about them called "braiding." That means that we can twist and cross the ribbons over each other in certain ways, and it won't mess up the overall shape of the ribbons.
Now, let's say we want to do some math with these braided ribbons. We can take different ribbons, twist them together, and get new ribbons! And just like with the regular ribbons, we can tie them in all sorts of knots and shapes.
But here's where it gets a bit more complicated. We don't just want to play with the ribbons themselves - we also want to think about how they interact with each other. For example, if we have two ribbons that are twisted together, and we want to untwist them, how can we do that? There are certain rules we follow, like making sure we don't accidentally tie any new knots in the ribbons.
A strongly ribbon category is a special kind of math set where we can do all of this twisting, braiding, and unbraiding with the ribbons. And because we have all of these rules to follow, we can be sure that we're doing the math correctly and getting the right answers!