Categories for the Working Mathematician is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. It was first published in 1971, and is based on his lectures on the subject given at the University of Chicago, the Australian National University, Bowdoin College, and Tulane University. It is widely regarded as the premier introduction to the subject. Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... This article is in need of attention from an expert on the subject. ... Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ... Samuel Eilenberg (September 30, 1913-January 30, 1998) was a Polish mathematician. ... 1971 (MCMLXXI) was a common year starting on Friday (the link is to a full 1971 calendar). ... The University of Chicago is a private university principally located in the Hyde Park neighborhood of Chicago, Illinois, founded in 1890 and opened in 1892. ... The Australian National University (ANU), is a university located in Canberra, the national capital of Australia. ... Bowdoin College is a private liberal arts college located in the coastal New England town of Brunswick, Maine. ... Tulane University is a private, nonsectarian, coeducational research university located in New Orleans, Louisiana. ...

Contents

The book is has ten chapters, which are:

Chapter I. Categories, Functors, and Natural Transformations.

Chapter II. Constructions on Categories.

Chapter III. Universals and Limits.

Chapter IV. Adjoints.

Chapter V. Limits.

Chapter VI. Monads and Algebras.

Chapter VII. Monoids.

Chapter VIII. Abelian Categories.

Chapter IX. Special Limits.

Chapter X. Kan Extensions.

Although it is the classic reference for category theory, some of the terminology is not standard. In particular, Mac Lane attempted to settle an ambiguity in usage for the terms epimorphism and monomorphism by introducing the terms epic and monic, but the distinction is not in common use. Did somebody just say functor? In category theory, a functor is a special type of mapping between categories. ... In category theory, an abstract branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i. ... In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions that are used in various parts of mathematics, like products and inverse limits. ... In mathematics, the term adjoint applies in several situations. ... In category theory, a monad or triple is a type of functor, together with two associated natural transformations. ... In mathematics, a monoidal category (or tensor category) is a 2-category with one object (a 2-monoid). ... In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have nice properties. ... Kan extensions are universal constructs in category theory, a branch of mathematics. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... Saunders Mac Lane (born 4 August 1909) is a US mathematician. ... In the context of abstract algebra or universal algebra, an epimorphism is simply a homomorphism onto or surjective homomorphism. ... In the context of abstract algebra or universal algebra, a monomorphism is simply an injective homomorphism. ...