**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

**Categories and Modules**

by

**Takahiro Kato**-

**viXra.org**

Modules and morphisms among them subsume categories and functors and provide more general framework to explore the theory of structures. In this book we generalize the basic notions and results of category theory using this framework of modules.

(

**3277**views)

**Introduction to Categories and Categorical Logic**

by

**Samson Abramsky, Nikos Tzevelekos**-

**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.

(

**7094**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.

(

**5181**views)

**Category Theory for the Sciences**

by

**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.

(

**1454**views)