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: Higher Operads, Higher CategoriesHigher Operads, Higher Categories
by - arXiv
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from topology, quantum algebra, mathematical physics, logic, and computer science.
(8813 views)
Book cover: An Introduction to Category Theory in Four Easy MovementsAn Introduction to Category Theory in Four Easy Movements
by - Manchester University
Notes for a course offered as part of the MSc. in Mathematical Logic. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.
(9437 views)
Book cover: Category Theory: A Gentle IntroductionCategory Theory: A Gentle Introduction
by - Logic Matters
I hope that what is here may prove useful to others starting to get to grips with category theory. This text is intended to be relatively accessible; in particular, it presupposes rather less mathematical background than some texts on categories.
(3692 views)
Book cover: Seven Sketches in Compositionality: An Invitation to Applied Category TheorySeven Sketches in Compositionality: An Invitation to Applied Category Theory
by - arXiv.org
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.
(2266 views)