Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

## A Characterization of Concept Lattices. Dual Concept Lattices

Christoph Schwarzweller
University of Tuebingen

### Summary.

In this article we continue the formalization of concept lattices following [6]. We give necessary and sufficient conditions for a complete lattice to be isomorphic to a given formal context. As a by-product we get that a lattice is complete if and only if it is isomorphic to a concept lattice. In addition we introduce dual formal concepts and dual concept lattices and prove that the dual of a concept lattice over a formal context is isomorphic to the concept lattice over the dual formal context.

#### MML Identifier: CONLAT_2

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [17] [8] [14] [2] [12] [18] [9] [16] [15] [1] [11] [4] [3] [19] [7] [10]

#### Contents (PDF format)

1. Preliminaries
2. The Characterization
3. Dual Concept Lattices

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