# Parents of Maps

Parents of maps are structures knowing a domain and a codomain. They are often used in automorphism group calculations where a map is returned from an automorphism group into the set of all automorphisms of some structure. Parents of maps all inherit from the type `PowMap`. The type `PowMapAut` which inherits from `PowMap` is the type which the parents of automorphisms inherit from.

There is also a power structure of maps (of type `PowStr`, similar to that of other structures) which is used as a common overstructure of the different parents.

## `Parent(m): Map -> PowMap`

The parent of $m$.

## `Domain(P): PowMap -> Str`

## `Codomain(P): PowMap -> Str`

The domain and codomain of the maps for which $P$ is the parent.

## `Maps(D, C): Str, Str -> PowMap`

## `Iso(D, C): Str, Str -> PowMap`

The parent of maps (or isomorphisms) from $D$ to $C$. `Iso` will only return a different structure to `Maps` if it has been specifically implemented for such maps.

## `Aut(S): Str -> PowMapAut`

The parent of automorphisms of $S$.