This word is a play on the many morphisms in mathematics, but cryptomorphism is only very distantly related to isomorphism, homomorphism, or morphisms.
Many common notions from mathematics (e.g. surjective, injective, free object, basis, finite representation, isomorphism) are definable purely in category theoretic terms (cf. monomorphism, epimorphism).
Specifically, an open immersion factors through an isomorphism with an open subscheme and a closed immersion factors through an isomorphism with a closed subscheme.
