2015/03/04 by Aleks Kissinger, Kissinger, Aleks, David Quick +1 · 1 citation
Computer Science · Physics and Astronomy · #Category Theory (math.CT) #Computational Physics and Python Applications #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1503.01348
openalex publication_date 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
!-graphs provide a means of reasoning about infinite families of string\ndiagrams and have proven useful in manipulation of (co)algebraic structures\nlike Hopf algebras, Frobenius algebras, and compositions thereof. However, they\nhave previously been limited by an inability to express families of diagrams\ninvolving non-commutative structures which play a central role in algebraic\nquantum information and the theory of quantum groups. In this paper, we fix\nthis shortcoming by offering a new semantics for non-commutative !-graphs using\nan enriched version of Penrose's abstract tensor notation.\n