Saunders Mac Lane: A Mathematical Autobiography

Biographies & Memoirs

Mac Lane, Saunders

Professionals & Academics

A K Peters/CRC Press

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general ized monoid. Chapters VI and VII explore this notion and its generaliza tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure (given by a tensor product) lead inter alia to the study of more convenient categories of topological spaces.

Categories for the Working Mathematician (Graduate Texts in Mathematics)

Science & Math

Mathematics

Springer, Verlag

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Categories for the Working Mathematician (Graduate Texts in Mathematics, 5)

Springer

Spectral Sequences And Homotopy: Lectures, Notes

Department Of Mathematics, University Of Chicago, Autumn 1953. Prepared With The Assistance Of A Grant By The Research Corporation.

Literature & Fiction

Halpern, Edward

Essays & Correspondence

Literary Licensing, LLC

Covering a period up to 1971, this selection of Saunders Mac Lane’s most distinguished papers takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century. Mac Lane was an extraordinary mathematician and a dedicated teacher who cared earnestly about the values of science and education. His life spanned nearly a century of mathematical progress. In his earlier years, he participated in the exciting developments in Göttingen. He studied under David Hilbert, Hermann Weyl, and Paul Bernays. Later, he contributed to the more abstract and general mathematical viewpoints which emerged in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept and theory of categories, together with Samuel Eilenberg, which has broad applications in different areas, in particular in topology and the foundations of mathematics.

Selected Papers (Springer Collected Works in Mathematics)

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

A Survey of Modern Algebra (Akp Classics)

Birkhoff, Garrett

Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Göttingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

History

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure (given by a tensor product) lead inter alia to the study of more convenient categories of topological spaces.

Categories for the working mathematician (Graduate texts in mathematics)

See the best price to sell, buy, or rent books by Mac Lane, Saunders. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Mac Lane, Saunders

See the best price to sell, buy, or rent books by Mac Lane, Saunders. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Saunders Mac Lane: A Mathematical Autobiography

Categories for the Working Mathematician (Graduate Texts in Mathematics)

Categories for the Working Mathematician (Graduate Texts in Mathematics, 5)

Spectral Sequences And Homotopy: Lectures, Notes

Spectral Sequences And Homotopy: Lectures, Notes

Selected Papers (Springer Collected Works in Mathematics)

A Survey of Modern Algebra (Akp Classics)

Saunders Mac Lane: A Mathematical Autobiography

A Survey of Modern Algebra (Akp Classics)

Categories for the working mathematician (Graduate texts in mathematics)