Universality: Definition and Examples (Bijections, Vector Space Bases, Free Groups) скачать в хорошем качестве

Universality: Definition and Examples (Bijections, Vector Space Bases, Free Groups)

Exploring and formally defining universality in category theory. Proof that bijections are always universal for the identity functor on the category of sets. Proof that the inclusion map of a basis into a vector space is universal for the forgetful functor from the category of vector spaces to the category of sets. Proof that the inclusion map of a set into the free group on that set is universal for the forgetful functor from the category of Groups to the category of Sets. For a detailed proof that the free group has the universal extension property with respect to its subsets, see here: www.math.unl.edu/~mbrittenham2/classwk/990s08/public/myasnikov.1.free.groups.pdf