An "almost" full embedding of the category of graphs into the category of abelian groups

Details An "almost" full embedding of the category of graphs into the category of abelian groups An "almost" full embedding of the category of graphs into the category of abelian groups

2011-04-29

arxiv.org/abs/1104.5689v1

Mathematics

Category Theory

16 pages

Scientific paper

We construct an embedding G of the category of graphs into the category of abelian groups such that for graphs X and Y we have Hom(GX,GY)=Z[Hom(X,Y)], the free abelian group whose basis is the set Hom(X,Y). The isomorphism is functorial in X and Y. The existence of such an embedding implies that, contrary to a common belief, the category of abelian groups is as complex and comprehensive as any other concrete category. We use this embedding to settle an old problem of Isbell whether every full subcategory of the category of abelian groups, which is closed under limits, is reflective. A positive answer turns out to be equivalent to weak Vopenka's principle, a large cardinal axiom which is not provable but believed to be consistent with standard set theory. Several known constructions in the category of abelian groups are obtained as quick applications of the embedding.

Affiliated with

Also associated with

No associations

Rating

An "almost" full embedding of the category of graphs into the category of abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An "almost" full embedding of the category of graphs into the category of abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An "almost" full embedding of the category of graphs into the category of abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-18175