This book introduces elementary category theory to an educated audience -- one not specialized in mathematics, but familiar with the basic set theory taught in high school.
Category theory shares a similar goal of unification with set theory, yet operates at a higher level of abstraction, while still making use of set theoretical foundations.
In set theory, the fundamental concept is membership: x belongs to A. In category theory, the focus shifts to the connections between objects within a category: P is linked to Q by an arrow.
We begin with an extensive chapter tracing the progression of mathematical abstraction, from the invention of numbers in the Paleolithic era to the emergence of group theory in the 19th century.
The book then presents the formal definition of a category, followed by common examples across various fields.
We cover diagrams and limits, functors and natural trans-formations, and conclude with two chapters reaching the edge of elementary theory: adjunctions and the Yoneda lemma.
The author: After scientific studies in France (丱ole Polytechnique) and the United States (PhD from Stanford University), Andr?Cabannes taught mathematics at the Massachusetts Institute of Technology. He has translated and authored numerous works in mathematics and physics.
Table of contents: https: //tinyurl.com/ymkpjscf
Preface: https: //tinyurl.com/d8668ztc
Free chapter: https: //tinyurl.com/puddyyhu
Index: https: //tinyurl.com/4kk6pknx
Erratum: https: //tinyurl.com/mrdhkre6
