Distributive semilattices as retracts of ultraboolean ones; functorial inverses without adjunction
General Mathematics
2007-05-23 v2 Category Theory
Abstract
A (v,0)-semilattice is ultraboolean, if it is a directed union of finite Boolean (v,0)-semilattices. We prove that every distributive (v,0)-semilattice is a retract of some ultraboolean (v,0)-semilattices. This is established by proving that every finite distributive (v,0)-semilattice is a retract of some finite Boolean (v,0)-semilattice, and this in a functorial way. This result is, in turn, obtained as a particular case of a category-theoretical result that gives sufficient conditions, for a functor , to admit a right inverse. The particular functor used for the abovementioned result about ultraboolean semilattices has neither a right nor a left adjoint.
Keywords
Cite
@article{arxiv.math/0409263,
title = {Distributive semilattices as retracts of ultraboolean ones; functorial inverses without adjunction},
author = {Friedrich Wehrung},
journal= {arXiv preprint arXiv:math/0409263},
year = {2007}
}