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 Eugenia Cheng, Aaron Lauda - University of Sheffield
This work gives an explanatory introduction to various definitions of higher-dimensional category. The emphasis is on ideas rather than formalities; the aim is to shed light on the formalities by emphasizing the intuitions that lead there.
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 Mikael Vejdemo-Johansson - University of St. Andrews
An introduction to category theory that ties into Haskell and functional programming as a source of applications. Topics: definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases, etc.
This book is an introduction to category theory, written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. It contains examples drawn from various branches of math.