Subsections

• Composition
• (Co)Domain and (Co)Kernel
• Function

Although compatible maps can be composed by repeated application, say g(f(x)), it is also possible to create a composite map.

f * g : Map, Map -> Map

Given a mapping f : A -> B, and a mapping g : B -> C, construct the composition h of the mappings f and g as the mapping h=g o f : A -> C.

The domain and codomain of any map can simply be accessed. Only certain intrinsic maps also support the formation of image, kernel and cokernel.

Domain(f) : Map -> Struct

The domain of the mapping f.

The codomain of the mapping f.

Given a mapping f with domain A and codomain B, return the image of A in B as a substructure of B. This function is currently available only for certain intrinsic maps.

Given the homomorphism f with domain A and codomain B, return the kernel of f as a substructure of A. This function is currently available only for certain intrinsic maps.

For a map given by a rule, it is possible to get access to the rule as a user defined function.

Function(f) : Map -> UserProgram

The function underlying the mapping f. Only available if f has been defined by the user by means of a rule map (ie an expression for the image under f of an arbitrary element of the domain).