**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

**Category Theory for Scientists**

by

**David I. Spivak**-

**arXiv**

We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based.

(

**8535**views)

**Categorical Homotopy Theory**

by

**Emily Riehl**-

**Cambridge University Press**

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Emily Riehl discusses two competing perspectives by which one typically first encounters homotopy (co)limits ...

(

**3160**views)

**Categories and Homological Algebra**

by

**Pierre Schapira**-

**UPMC**

These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.

(

**8795**views)

**Category Theory Lecture Notes**

by

**Daniele Turi**-

**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.

(

**10182**views)