The fundamental duality of partially ordered sets
type: Item
instance of: scholarly article
title: The fundamental duality of partially ordered sets
zbMATH Open document ID: 0653.06003
DOI: 10.1007/BF00143898
author: Bernhard Banaschewski
author: Günter Bruns
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: The authors embed posets, lattices, and frames in the category \(\underset \tilde{} P\) of posets with an arbitrary family of joins and an arbitrary family of meets distinguished. (Thus, posketches.) Universal maps from objects of \(\underset \tilde{} P\) to posets of all subsets with unions and intersections were constructed by the second author in J. Reine Angew. Math. 209, 167-200, and 210, 1-23 (1962; Zbl 0148.012). This is now amplified to a Galois connection (or imperfect ``duality'') extending several familiar connections and dualities. The objects of the second category generalize topological spaces and closure spaces.
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 4065054
zbMATH Keywords: category of posets
zbMATH Keywords: lattices
zbMATH Keywords: frames
zbMATH Keywords: posketches
zbMATH Keywords: Galois connection
zbMATH Keywords: dualities
reviewed by: J. R. Isbell
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00143898
OpenAlex ID: W1969925243
description: scientific article; zbMATH DE number 4065054