What the pony is ...

[vh]

Post random, confusing terms here.

Isomorphism

http://en.wikipedia.org/wiki/Isomorphism

In abstract algebra, an isomorphism[1] is a bijective homomorphism.[2] Two mathematical structures are said to be isomorphic if there is an isomorphism between them.

In category theory, an isomorphism is a morphism f: X → Y in a category for which there exists an "inverse" f −1: Y → X, with the property that both f −1f = idX and f f −1 = idY.[3]

oh i completely understand now 

[deoxy99]

I've been completely enlightened. It all makes sense now.