Categorical quotient
Alright kiddo, let me explain categorical quotient to you.
Imagine you have a bunch of toys that are similar but have some differences, like different colors or shapes. You want to put them in groups based on their similarities, so you can organize them neatly. You start putting all the toys with the same color together, all the toys with the same shape together, and so on.
In math, we call these groups "categories". When we have a set of things and we want to put them into categories based on their similarities, we're doing something called "categorization".
Now, let's say you have some toys that are exactly the same, but you have duplicates of them. You don't want to group them together and count them multiple times, because it will mess up your organization. So what do you do?
You create a new category called "unique toys", and you put only one of each duplicate toy in that category. Now you have a neat and organized system that won't count any toy twice.
In math, we call this process "taking the categorical quotient". We take a set of things and divide them into categories based on their similarities, but we don't want duplicates. So we create a new category that only includes unique things, and put one of each duplicate thing in there.
Does that make sense, kiddo?
Imagine you have a bunch of toys that are similar but have some differences, like different colors or shapes. You want to put them in groups based on their similarities, so you can organize them neatly. You start putting all the toys with the same color together, all the toys with the same shape together, and so on.
In math, we call these groups "categories". When we have a set of things and we want to put them into categories based on their similarities, we're doing something called "categorization".
Now, let's say you have some toys that are exactly the same, but you have duplicates of them. You don't want to group them together and count them multiple times, because it will mess up your organization. So what do you do?
You create a new category called "unique toys", and you put only one of each duplicate toy in that category. Now you have a neat and organized system that won't count any toy twice.
In math, we call this process "taking the categorical quotient". We take a set of things and divide them into categories based on their similarities, but we don't want duplicates. So we create a new category that only includes unique things, and put one of each duplicate thing in there.
Does that make sense, kiddo?
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