Distributive semilattices as retracts of ultraboolean ones; functorial inverses without adjunction

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dc.creatorWehrung, Friedrich
dc.date2004-09-15
dc.date2005-08-30
dc.date.accessioned2026-07-07T05:12:09Z
dc.date.available2026-07-07T05:12:09Z
dc.descriptionA (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.
dc.identifierhttps://arxiv.org/abs/math/0409263
dc.identifierhttp://arxiv.org/abs/math/0409263
dc.identifierJournal of Pure and Applied Algebra 202, no. 1--3 (2005) 201--229
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72484
dc.subjectGeneral Mathematics
dc.subjectCategory Theory
dc.subjectAMS: 18A30, 18A25, 18A20, 06A12, 06D05, 08B25, 18A40
dc.titleDistributive semilattices as retracts of ultraboolean ones; functorial inverses without adjunction
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