An Morphism is a mapping between two objects of the same type that preserves structure.
If the mapping can be reversed by an inverse mapping then the Morphism is an Isomorphism. An isomorphism is a Morphism that is Bijective.
Appendix A
One type of morphism, Automorphism, doesn’t completely adhere to the general definition given above.
This doesn’t surprise us. We defined cats as being a creature that doesn’t like the water; tigers and cheetahs love to swim.
Appendix B
Assume we have a triangle with vertices labeled A, B and C. We rotate the triangle 120 degrees such that:
- A moves to old B
- B moves to old C
- C moves to old A
The triangle looks the same as it did before. This means something but we aren’t quite ready to discuss it…
Alternately, we say that we can map A–>B, B–>C and C–>A.
Appendix B
To use language we used in in Geometry class, we might say that A, B and C are corresponding points.
We have a rule that says, something is (word not given yet) if we do an action on an object and all points of the object move to corresponding points.
If all points move to corresponding points then the object will look the same in photographs taken before and after the action was done.
Rob Sterling 