Dynamical Systems and Sheaves
by D. I. Spivak, C. Vasilakopoulou, P. Schultz
Publisher: arXiv 2016
Number of pages: 65
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include discrete, continuous, and hybrid dynamical systems. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems.
Home page url
Download or read it online for free here:
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.
by Peter W. Michor - Springer
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
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.
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.