Combinatorics and Algebra of Tensor Calculus
by Sen Hu, Xuexing Lu, Yu Ye
Publisher: arXiv 2015
Number of pages: 88
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.
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by D.E. Rydeheard, R.M. Burstall
The book is a bridge-building exercise between computer programming and category theory. Basic constructions of category theory are expressed as computer programs. It is a first attempt at connecting the abstract mathematics with concrete programs.
by Jaap van Oosten - University of Utrecht
Contents: Categories and Functors; Natural transformations; (Co)cones and (Co)limits; A little piece of categorical logic; Adjunctions; Monads and Algebras; Cartesian closed categories and the lambda-calculus; Recursive Domain Equations.
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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.