Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape."
Formally, an isomorphism in a category is a morphism 
with a morphism 
satisfying 
and 
, where 
and 
denote the identity morphisms
of 
and 
(The Stacks Project Authors 2026). Informally, an isomorphism
is a map that preserves sets and relations among elements. "
is isomorphic to 
" is written 
. Unfortunately, this symbol is also used to denote geometric
congruence.
An isomorphism from a set of elements onto itself is called an automorphism.
