If is bijective and is any map s.t
then is bijective.
the compostion is a function that goes from Y to Y. I am pretty sure it's onto, since f is onto. It's injective because g uniquely determines what the composition ends up as.
(we are sending to a unique function, that goes from
I think the real question I'm asking is, does this define an isomorphism?
Sorry if this is unclear. I tried my best to word it coherently. I will try to clarify if needed.