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

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The discussion centers on whether a morphism y->x can be inferred from x->y. It is clarified that while a bijective morphism allows for this implication, it is not universally applicable. The existence of morphisms between objects in a category does not guarantee a direct reverse relationship. Instead, there may be a set of morphisms from y to x, which could be trivial. The relationship between morphisms is nuanced and not simply reciprocal.
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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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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