Focusing on the evolution of mathematics throughout the twentieth century, this collection showcases Saunders Mac Lane's influential papers up to 1971. A remarkable mathematician and educator, Mac Lane was deeply involved in groundbreaking developments in Göttingen and studied under renowned figures like David Hilbert. His significant contributions include the creation of category theory alongside Samuel Eilenberg, which has far-reaching implications in topology and foundational mathematics, reflecting his commitment to advancing scientific understanding and education.
Focusing on the life of an extraordinary mathematician, this autobiography chronicles key milestones in twentieth-century mathematics. Through personal anecdotes and reflections, it provides insights into the evolution of mathematical thought and the author's influential contributions to the field. The narrative not only highlights significant events but also offers a glimpse into the intellectual landscape that shaped modern mathematics.
Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathematicians 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 generalized monoid. Chapters VI and VII explore this notion and its generalizations. 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
