Rewriting the elements in the intersection of the kernels of two morphisms between free groups
Group Theory
2021-03-09 v1 Algebraic Topology
Category Theory
Abstract
Let F be the free group functor, left adjoint to the forgetful functor between the category of groups GRP and the category of sets SET. Let f from A to B, and h from A to C be two functions in SET and let Ker(F(f)) and Ker(F(h)) be the kernels of the induced morphisms between free groups. Provided that the kernel pairs Eq(f) and Eq(h) of f and h permute (such as it is the case when the pushout of f and h is a double extension in SET), this short article describes a method to rewrite a general element in the intersection of Ker(F(f)) and Ker(F(g)) as a product of generators in A which is (f,h)-symmetric in the sense of the higher covering theory of racks and quandles.
Keywords
Cite
@article{arxiv.2103.04793,
title = {Rewriting the elements in the intersection of the kernels of two morphisms between free groups},
author = {François Renaud},
journal= {arXiv preprint arXiv:2103.04793},
year = {2021}
}