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# Notes Exercise 2.15

What kind of sorting does the mapping out of $$C$$ to the walking isomorphism category define?

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Hi @JakeGillberg, can you give the background on what is C and is meant by the mapping out of it. I don’t have the notes at hand, but I’m guessing that the setup is something like this?

The walking isomorphism is defined by the diagram I that you gave. C is an arbitrary category. The mapping out of C is some functor F from C to I. So the problem is asking about what structure (sorting) is induced by F on C?

Comment Source:Hi @JakeGillberg, can you give the background on what is C and is meant by the mapping out of it. I don’t have the notes at hand, but I’m guessing that the setup is something like this? The walking isomorphism is defined by the diagram I that you gave. C is an arbitrary category. The mapping out of C is some functor F from C to I. So the problem is asking about what structure (sorting) is induced by F on C?
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edited January 2020

Yup, you got it! My intuition is that splitting Obj_C into any desired two (empty or non-empty) sets picks a functor F -> I, but I'm wondering if there is some structure I am not seeing.

Comment Source:Yup, you got it! My intuition is that splitting Obj_C into any desired two (empty or non-empty) sets picks a functor F -> I, but I'm wondering if there is some structure I am not seeing.