Logo

Combinatorics and Algebra of Tensor Calculus

Small book cover: Combinatorics and Algebra of Tensor Calculus

Combinatorics and Algebra of Tensor Calculus
by

Publisher: arXiv
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.

Home page url

Download or read it online for free here:
Download link
(860KB, PDF)

Similar books

Book cover: Functors and Categories of Banach SpacesFunctors and Categories of Banach Spaces
by - 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.
(5181 views)
Book cover: Notes on Categories and GroupoidsNotes on Categories and Groupoids
by - Van Nostrand Reinhold
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(9104 views)
Book cover: Category Theory Lecture NotesCategory Theory Lecture Notes
by - University of Edinburgh
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.
(5929 views)
Book cover: Introduction to Categories and Categorical LogicIntroduction to Categories and Categorical Logic
by - arXiv
These notes provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
(6370 views)