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 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.
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.
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.
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.