From an algebraical point of view, the most important mappings are those which are compatible with a structure. For Magmas, Groups and Rings, GAP supports the following four types of such mappings:
1. General mappings that respect multiplication
2. General mappings that respect addition
3. General mappings that respect scalar mult.
4. General mappings that respect multiplicative and additive structure
(Very technical note: GAP defines categories IsSPGeneralMapping and
IsNonSPGeneralMapping. The distinction between these is orthogonal to the
Structure Compatibility described here and should not be confused.)
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GAP 4 manual