Categories for the Working Mathematician: 5 (Graduate Texts in Mathematics) - Softcover

MacLane, Saunders

Softcover

ISBN 10: 0387900365 ISBN 13: 9780387900360

Verlag: Springer-Verlag New York Inc., 1971

Inhaltsangabe

Book by MacLane Saunders

Über diesen Titel

Reseña del editor

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.

Details zur Ausgabe

• Verlag: Springer-Verlag New York Inc.
• Erscheinungsdatum: 1971
• ISBN 10: 0387900365
• ISBN 13: 9780387900360
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 271