ABSTRACT
T he universal coefficient theorem starts with a homomorphism α from the cohomology Hn(X,G) of a space X with coefficients in a group G:
α: Hn(X,G ) Hom(Hn(X ),G ).
Moreover, this homomorphism behaves well for continuous maps f :X Y of spaces. In the last chapter, I said that we gave this simple commutativity behavior the name natural. This is not really accurate. We didn’t come up with this term-we just followed the informal terminology then used for such matters.
