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
Seminar on Triples and Categorical Homology Theoryby B. Eckmann - Springer
This volume concentrates a) on the concept of 'triple' or standard construction with special reference to the associated 'algebras', and b) on homology theories in general categories, based upon triples and simplicial methods.
(11938 views)
Category Theory for the Sciencesby David I. Spivak - The MIT Press
This book shows that category theory can be useful outside of mathematics as a flexible modeling language throughout the sciences. Written in an engaging and straightforward style, the book is rigorous but accessible to non-mathematicians.
(7826 views)
Functors and Categories of Banach Spacesby Peter W. Michor - Springer
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
(10999 views)
Basic Concepts of Enriched Category Theoryby Max Kelly - Cambridge University Press
The book presents a selfcontained account of basic category theory, assuming as prior knowledge only the most elementary categorical concepts. It is designed to supply a connected account of the theory, or at least of a substantial part of it.
(13671 views)