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 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.