F. William Lawvere, Stephen H. Schanuel Conceptual Mathematics A First Introduction To Categories ( 2009, Cambridge University Press) ( 1)
Category Theory first introduction
Introduction To Category Theory
Introduction To Category Theory by Steve Awodey, 2010, Oxford University Press, USA, Oxford University Press edition,
Category theory for computing science
Category theory for computing science by Michael Barr, 1990, Prentice Hall edition, in English
Category Theory for Programmers: The Preface
Table of Contents Part One Category: The Essence of Composition Types and Functions Categories Great and Small Kleisli Categories Products and Coproducts Simple Algebraic Data Types Functors Functo…
A categorical manifesto
This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical discussion.
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. A feedback form for typos, comments, questions, and suggestions is available here: https://docs.google.com/document/d/160G9OFcP5DWT8Stn7TxdVx83DJnnf7d5GML0_FOD5Wg/edit
Computational category theory
Computational category theory by D. E. Rydeheard, 1988, Prentice Hall edition, in English
Conceptual mathematics: a first introduction to categories
Conceptual mathematics by F. W. Lawvere, 2009, Cambridge University Press edition, in English - 2nd ed.
Basic Category Theory
This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its heart is the concept of a universal property, important throughout mathematics. After a chapter introducing the basic definitions, separate chapters present three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties the three together. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.
Categories for Machine Learning
This seminar series seeks to promote the learning and use of Category Theory by Machine Learning Researchers
Category: The Essence of Composition
I was overwhelmed by the positive response to my previous post, the Preface to Category Theory for Programmers. At the same time, it scared the heck out of me because I realized what high expectati…
Basic Concepts of Enriched Category Theory
Originally published as: Cambridge University Press, Lecture Notes in Mathematics 64, 1982.
Emily Riehl
Website for `Category theory in context' published in 2016 by Dover Publications.
Generalised algebraic theories and contextual categories
Category Theory: The Beginner’s Introduction