Combinatorics and algebra of tensor calculus

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.

88 pages

References in corpus (3)

• Exact entanglement renormalization for string-net models
• Topological conformal field theories and Calabi-Yau categories
• Noncommutative geometry through monoidal categories