A Gentle Introduction to Category Theory: the calculational approach
by Maarten M. Fokkinga
Publisher: University of Twente 1994
Number of pages: 80
In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. This text differs from most other introductions to category theory in the calculational style of the proofs, the restriction to applications within algorithmics, and the omission of many additional concepts and facts that I consider not helpful in a first introduction to category theory.
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by Max Kelly - Cambridge University Press
The book presents a selfcontained account of basic category theory, assuming as prior knowledge only the most elementary categorical concepts. It is designed to supply a connected account of the theory, or at least of a substantial part of it.
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 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.