**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

**Higher Operads, Higher Categories**

by

**Tom Leinster**-

**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.

(

**7407**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.

(

**7020**views)

**Banach Modules and Functors on Categories of Banach Spaces**

by

**J. Cigler, V. Losert, P.W. Michor**-

**Marcel Dekker Inc**

This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.

(

**5280**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.

(

**1380**views)