**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.

(

**8813**views)

**An Introduction to Category Theory in Four Easy Movements**

by

**A. Schalk, H. Simmons**-

**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)

**Category Theory: A Gentle Introduction**

by

**Peter Smith**-

**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)

**Seven Sketches in Compositionality: An Invitation to Applied Category Theory**

by

**Brendan Fong, David I Spivak**-

**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)