Basic Category Theory
by Tom Leinster
Publisher: arXiv 2016
Number of pages: 191
This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics.
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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 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 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.
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.