Skip to content

CT: Isomorphism


If two things are isomorphic, then for many intents and purposes they are the same.

Category Theory

In category theory, an isomorphism is a morphism which can be inverted. f

\forall c. \forall f : a \rightarrow b\quad g : b \rightarrow a. g \circ f = id
\forall c. \forall f : a \rightarrow b\quad g : b \rightarrow a. f \circ g = id

where id is the identity morphism.

A pair of objects is isomorphic if an isomorphism exists between them. This practically means that objects which are isomorphic to each other are the same.

Isomorphism is the generalisation of the concept of bijection from the category Set to other categories.

In software, A pair of types with the same cardinality will always be isomorphic