| 书目名称 | Categories for the Working Mathematician | | 编辑 | Saunders Mac Lane | | 视频video | http://file.papertrans.cn/223/222540/222540.mp4 | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | 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 ti | | 出版日期 | Textbook 19711st edition | | 关键词 | Adjoint functor; Categories; Coproduct; algebra; category theory; colimit; equalizer; semigroup; transformat | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-9839-7 | | isbn_ebook | 978-1-4612-9839-7Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1971 |
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