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 B. Eckmann - Springer
This volume concentrates a) on the concept of 'triple' or standard construction with special reference to the associated 'algebras', and b) on homology theories in general categories, based upon triples and simplicial methods.
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.
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.
by Bartosz Milewski - unglue.it
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming.