Category Theory and Functional Programming
by Mikael Vejdemo-Johansson
Publisher: University of St. Andrews 2012
Number of pages: 99
This text is intended to provide an introduction to Category Theory that ties into Haskell and functional programming as a source of examples and applications. Topics covered: The definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases of these, adjunctions, freeness and presentations as categorical constructs, monads and Kleisli arrows, recursion with categorical constructs.
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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 David I. Spivak - arXiv
We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based.
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.
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.