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In this paper we are interested in the dual composition of two relations. The dual composition is defined to be the composition of relations on the dual order structure of a distributive allegory if it exists. We investigate this operation and the corresponding algebraic/categorical structures. In particular, we show that its existence guarantees that complemented relations are closed under composition, and we investigate when the dual composition of two univalent relations is again univalent.

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On the Dual Composition of Relations

  • 会议论文

  • 发表日期：

    2026年

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  • Michael Winter

摘要

In this paper we are interested in the dual composition of two relations. The dual composition is defined to be the composition of relations on the dual order structure of a distributive allegory if it exists. We investigate this operation and the corresponding algebraic/categorical structures. In particular, we show that its existence guarantees that complemented relations are closed under composition, and we investigate when the dual composition of two univalent relations is again univalent.