Does the morphism above imply the other way around, ie, y->x?

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The discussion centers on the implications of morphisms in category theory, specifically whether a morphism from y to x can be inferred from a morphism from x to y. It is established that while a morphism x → y does not imply y → x, there exists a set of morphisms from y to x, which may be trivial. The conversation emphasizes the importance of bijective relationships and homomorphisms in understanding these implications.

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my question: does the morphism above imply the other way around, ie, y->x?
 
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Well...if it's bijective...yes...and it's a homomorphism...I guess...[?]
 
Originally posted by loop quantum gravity
my question: does the morphism above imply the other way around, ie, y->x?

there is a set of morphisms between any objects in your category. so while it is not correct to say that x-->y implies y-->x, it is true that there exists a set of morphisms (which might be trivial) from y-->x. but this is not dependent on the morphisms from x-->y
 

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