2004/09/30 by Friedrich Wehrung
Mathematics · #math.GM #math.CT #msc:18A30 #msc:18A25 #msc:18A20 #msc:06A12 #msc:06D05 #msc:08B25 #msc:18A40
published as Journal of Pure and Applied Algebra 202, no. 1--3 (2005) 201--229
arxiv created 2005/08/30 · arxiv updated 2009/12/01
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 Pi, to admit a right inverse. The particular functor Pi used for the abovementioned result about ultraboolean semilattices has neither a right nor a left adjoint.