Combinatorics and Algebra of Tensor Calculus
by Sen Hu, Xuexing Lu, Yu Ye
Publisher: arXiv 2015
Number of pages: 88
Description:
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.
Download or read it online for free here:
Download link
(860KB, PDF)
Similar books
Higher Topos Theoryby Jacob Lurie - Princeton University Press
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
(18146 views)
Category Theory Lecture Notesby Michael Barr, Charles Wells
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
(15224 views)
Notes on Category Theory with examples from basic mathematicsby Paolo Perrone - arXiv
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced mathematics.
(3576 views)
Categories, Types, and Structuresby Andrea Asperti, Giuseppe Longo - MIT Press
Here is an introduction to category theory for the working computer scientist. It is a self-contained introduction to general category theory and the mathematical structures that constitute the theoretical background.
(21990 views)