The book "Categories for the Working Mathematician" by Saunders Mac Lane is a comprehensive text on category theory, aimed at mathematicians working in various fields. It is the second edition of the book, which includes two new chapters on symmetric monoidal categories and braided monoidal categories, as well as 2-categories and higher-dimensional categories. The book also includes an expanded bibliography to reflect recent advances in the field. The first edition of the book was published in 1971 and aimed to present the fundamental ideas and methods of category theory that can be effectively used by mathematicians in various fields. The book is structured into chapters that cover the basic concepts of category theory, such as categories, functors, natural transformations, and adjoint functors. It also explores more advanced topics, including monoids, monoidal categories, and abelian categories. The book is divided into several parts, each focusing on different aspects of category theory. The first part introduces the basic concepts of categories, functors, and natural transformations. The second part discusses constructions on categories, including duality, contravariance, and products of categories. The third part covers universals and limits, including universal arrows, the Yoneda lemma, and coproducts and colimits. The fourth part explores adjoints, including adjunctions, examples of adjoints, and transformations of adjoints. The fifth part focuses on limits, including the creation of limits, limits by products and equalizers, and the preservation of limits. The sixth part discusses monads and algebras, including monads in a category, algebras for a monad, and Beck's theorem. The seventh part covers monoids, including monoidal categories, coherence, and actions. The eighth part discusses abelian categories, including kernels and cokernels, additive categories, and diagram lemmas. The ninth part covers special limits, including filtered limits, interchange of limits, and ends. The tenth part discusses Kan extensions, including adjoints and limits, weak universality, and pointwise Kan extensions. The eleventh part explores symmetry and braiding in monoidal categories, including symmetric monoidal categories, monoidal functors, and braided coherence. The twelfth part discusses structures in categories, including internal categories, the nerve of a category, 2-categories, and bicategories. The book also includes an appendix on foundations, a table of standard categories, a table of terminology, a bibliography, and an index.The book "Categories for the Working Mathematician" by Saunders Mac Lane is a comprehensive text on category theory, aimed at mathematicians working in various fields. It is the second edition of the book, which includes two new chapters on symmetric monoidal categories and braided monoidal categories, as well as 2-categories and higher-dimensional categories. The book also includes an expanded bibliography to reflect recent advances in the field. The first edition of the book was published in 1971 and aimed to present the fundamental ideas and methods of category theory that can be effectively used by mathematicians in various fields. The book is structured into chapters that cover the basic concepts of category theory, such as categories, functors, natural transformations, and adjoint functors. It also explores more advanced topics, including monoids, monoidal categories, and abelian categories. The book is divided into several parts, each focusing on different aspects of category theory. The first part introduces the basic concepts of categories, functors, and natural transformations. The second part discusses constructions on categories, including duality, contravariance, and products of categories. The third part covers universals and limits, including universal arrows, the Yoneda lemma, and coproducts and colimits. The fourth part explores adjoints, including adjunctions, examples of adjoints, and transformations of adjoints. The fifth part focuses on limits, including the creation of limits, limits by products and equalizers, and the preservation of limits. The sixth part discusses monads and algebras, including monads in a category, algebras for a monad, and Beck's theorem. The seventh part covers monoids, including monoidal categories, coherence, and actions. The eighth part discusses abelian categories, including kernels and cokernels, additive categories, and diagram lemmas. The ninth part covers special limits, including filtered limits, interchange of limits, and ends. The tenth part discusses Kan extensions, including adjoints and limits, weak universality, and pointwise Kan extensions. The eleventh part explores symmetry and braiding in monoidal categories, including symmetric monoidal categories, monoidal functors, and braided coherence. The twelfth part discusses structures in categories, including internal categories, the nerve of a category, 2-categories, and bicategories. The book also includes an appendix on foundations, a table of standard categories, a table of terminology, a bibliography, and an index.