Isomorphism

Abstract

This chapter is about the things that matter and the things that do not matter. Consider this. In the last chapter, you learned that D ₄ means the symmetry group of a square. Did you respond by asking: “Which square? Where is it centered? How big is it? Is it upright or tilted? Is it green or purple?” Later, when you studied the symmetry group of an infinite strip of Gs, did you ask: “How tall are the Gs? How far apart are they spaced? What color are they? You probably did NOT ask these questions because you intuitively sensed that their answers do not matter. In exactly what sense do these things not matter? To focus on what does matter, we will need a more precise way of understanding exactly what does not matter.That is the purpose of this chapter. That is the purpose of an isomorphism.