Partitioned Binary Relations

  • Paul Martin
  • Volodymyr Mazorchuk

Abstract

We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of the category of partitioned binary relations and show that it gives rise to classical one-parameter deformations of partition, Brauer and Temperley-Lieb categories. Finally, we describe a factorization of partitioned binary relations into a product of certain idempotents and pairs of usual binary relations.
Published
2013-09-01
How to Cite
Martin, P., & Mazorchuk, V. (2013). Partitioned Binary Relations. MATHEMATICA SCANDINAVICA, 113(1), 30-52. https://doi.org/10.7146/math.scand.a-15480
Section
Articles