Although compatible maps can be composed by repeated application, say g(f(x)), it is also possible to create a composite 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 f : A -> C.
Returns the maps which were composed to form f.
The domain and codomain of any map can simply be accessed. Only for some intrinsic maps and for maps with certain domains and codomains, also the formation of image, kernel and cokernel is available.
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 supported only for some intrinsic maps and for maps with certain domains and codomains.
Given the homomorphism f with domain A and codomain B, return the kernel of f as a substructure of A. This function is currently supported only for some intrinsic maps and for maps with certain domains and codomains.
The inverse map of the map m.
For a map given by a rule, it is possible to get access to the rule as a user defined function.
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).