Presentations of Diagram Categories

  • Mengwei Hu Sichuan University
Keywords: rook category; planar rook category; rook-Brauer category; Motzkin category; partition category; monoidal category; diagrammatic algebra


We describe the planar rook category, the rook category, the rook-Brauer category, and the Motzkin category in terms of generators and relations. We show that the morphism spaces of these categories have linear bases given by planar rook diagrams, rook diagrams, rook-Brauer diagrams, and Motzkin diagrams.

Author Biography

Mengwei Hu, Sichuan University

Mengwei Hu is a 4th-year undergraduate majoring in Mathematics at Sichuan University, Chengdu, China. Her interests are representation theory and quantum algebra. She is planning to do a Ph.D. upon graduation.

How to Cite
Hu, M. (2019). Presentations of Diagram Categories. The PUMP Journal of Undergraduate Research, 3, 1-25. Retrieved from