"Categories for the Working Mathematician" provides 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. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis ...
This book is an introduction to the theory of toposes, as first developed by Grothendieck and later developed by Lawvere and Tierney. Beginning with several illustrative examples, the book explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to ...
This is a systematic introduction to homological algebra, starting with basic notions in abstract algebra and category theory and continuing with an up-to-date treatment of various advanced topics. The main ideas are introduced gradually with many examples illustrating why they are needed and what they can do. In conclusion, the book treats ...
Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the 20th century. During the earlier part of the 20th century he participated in the exciting happenings in Gottingen - the Mecca of mathematics. Later, he contributed to the more abstract and general mathematical viewpoints ...
This text introduces abstract algebra using familiar and concrete examples that illustrate each new concept as it is presented. It includes the coverage of such topics as the role of careful proof in algebra; linear algebra as grounded in geometry; groups as expressions of symmetry; subgroups and subsystems leading to lattice theory; and more. To ...
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