The closest I have found is type conversion in a computer language, for example back and forth between integers and real numbers (floats). Is this a good way to think of it? Is there a more general way of understanding that is less technical?
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I don’t think that is a good way of thinking about it.
Adjoint functors are a concept in category theory, probably the most abstract branch of math. It would be pretty simple to list some examples of adjoint functors. However, all require math background. Nonetheless, I’ll try to ELI5 [currying](https://en.wikipedia.org/wiki/Currying), the most common example.
Suppose you are tasked to do a survey about how a class of children rate different candies. If you know the names of kids, the types of candies, and the rating scale to use, there are two equally good options from information-gathering point of view.
First, is to print a spreadsheet where rows correspond to children, columns to candy, and give it to the class with instructions to fill in their rating to the cells in the table.
Second, is to print an individual survey with check boxes ([something like this](https://image.shutterstock.com/shutterstock/photos/20682616/display_1500/stock-photo-survey-box-check-box-checked-list-isolated-white-background-customer-questionnaire-checkbox-tick-20682616.jpg)) for each kid and hand them over with instructions to tick the boxes.
With either you have the same information available. However, the methods are different.
In math terms, if *A* is the set of kids, *B* is the set of candies, *C* is the set of ratings, the spreadsheet represents the product of *A* and *B* and filling out the speadsheet represents a function that assigns a value to every cell. The result is a **function where the input is a pair of variables, one from** ***A*** **and one from** ***B*****, and the output is an element of** ***C.***
On the other hand, each filled out survey paper describes an assignment of rating to each candy, so it’s a function from *B* to *C.* You receive one such slip of paper from every kid. The result is **a function where the input is one variable from** ***A*** **and the output is a function from** ***B*** **to** ***C.***
As explaimed earlier they are equivalent methods, so
>function from (the product of *A* and *B*) to *C =* function from *A* to (a function from *B* to *C*)
This relates two functors in an interesting way, the functor of “taking a product of a given set with the set *B*” and the functor “for a given set form the set of all functions from *B* to that set”. These two functors are called adjoint functors.
I don’t think that is a good way of thinking about it.
Adjoint functors are a concept in category theory, probably the most abstract branch of math. It would be pretty simple to list some examples of adjoint functors. However, all require math background. Nonetheless, I’ll try to ELI5 [currying](https://en.wikipedia.org/wiki/Currying), the most common example.
Suppose you are tasked to do a survey about how a class of children rate different candies. If you know the names of kids, the types of candies, and the rating scale to use, there are two equally good options from information-gathering point of view.
First, is to print a spreadsheet where rows correspond to children, columns to candy, and give it to the class with instructions to fill in their rating to the cells in the table.
Second, is to print an individual survey with check boxes ([something like this](https://image.shutterstock.com/shutterstock/photos/20682616/display_1500/stock-photo-survey-box-check-box-checked-list-isolated-white-background-customer-questionnaire-checkbox-tick-20682616.jpg)) for each kid and hand them over with instructions to tick the boxes.
With either you have the same information available. However, the methods are different.
In math terms, if *A* is the set of kids, *B* is the set of candies, *C* is the set of ratings, the spreadsheet represents the product of *A* and *B* and filling out the speadsheet represents a function that assigns a value to every cell. The result is a **function where the input is a pair of variables, one from** ***A*** **and one from** ***B*****, and the output is an element of** ***C.***
On the other hand, each filled out survey paper describes an assignment of rating to each candy, so it’s a function from *B* to *C.* You receive one such slip of paper from every kid. The result is **a function where the input is one variable from** ***A*** **and the output is a function from** ***B*** **to** ***C.***
As explaimed earlier they are equivalent methods, so
>function from (the product of *A* and *B*) to *C =* function from *A* to (a function from *B* to *C*)
This relates two functors in an interesting way, the functor of “taking a product of a given set with the set *B*” and the functor “for a given set form the set of all functions from *B* to that set”. These two functors are called adjoint functors.
I don’t think that is a good way of thinking about it.
Adjoint functors are a concept in category theory, probably the most abstract branch of math. It would be pretty simple to list some examples of adjoint functors. However, all require math background. Nonetheless, I’ll try to ELI5 [currying](https://en.wikipedia.org/wiki/Currying), the most common example.
Suppose you are tasked to do a survey about how a class of children rate different candies. If you know the names of kids, the types of candies, and the rating scale to use, there are two equally good options from information-gathering point of view.
First, is to print a spreadsheet where rows correspond to children, columns to candy, and give it to the class with instructions to fill in their rating to the cells in the table.
Second, is to print an individual survey with check boxes ([something like this](https://image.shutterstock.com/shutterstock/photos/20682616/display_1500/stock-photo-survey-box-check-box-checked-list-isolated-white-background-customer-questionnaire-checkbox-tick-20682616.jpg)) for each kid and hand them over with instructions to tick the boxes.
With either you have the same information available. However, the methods are different.
In math terms, if *A* is the set of kids, *B* is the set of candies, *C* is the set of ratings, the spreadsheet represents the product of *A* and *B* and filling out the speadsheet represents a function that assigns a value to every cell. The result is a **function where the input is a pair of variables, one from** ***A*** **and one from** ***B*****, and the output is an element of** ***C.***
On the other hand, each filled out survey paper describes an assignment of rating to each candy, so it’s a function from *B* to *C.* You receive one such slip of paper from every kid. The result is **a function where the input is one variable from** ***A*** **and the output is a function from** ***B*** **to** ***C.***
As explaimed earlier they are equivalent methods, so
>function from (the product of *A* and *B*) to *C =* function from *A* to (a function from *B* to *C*)
This relates two functors in an interesting way, the functor of “taking a product of a given set with the set *B*” and the functor “for a given set form the set of all functions from *B* to that set”. These two functors are called adjoint functors.
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