f:x->y ?

[MathematicalPhysicist]

my question: does the morphism above imply the other way around, ie, y->x?

[bogdan]

Well...if it's bijective...yes...and it's a homomorphism...I guess...[?]

[lethe]

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