Combinatorics and algebra of tensor calculus

2015/01/08 by S. T. Hu, Hu, Sen, Xuexing Lu +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1501.01790

openalex publication_date 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.

Citations

• Noncommutative geometry through monoidal categories
• Physics, Topology, Logic and Computation: A Rosetta Stone
• Topological conformal field theories and Calabi-Yau categories

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