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Titlebook: Categories for the Working Mathematician; Saunders Mac Lane Textbook 1978Latest edition Springer Science+Business Media New York 1978 Adjo

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發(fā)表于 2025-3-21 19:27:28 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Categories for the Working Mathematician
編輯Saunders Mac Lane
視頻videohttp://file.papertrans.cn/223/222541/222541.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Categories for the Working Mathematician;  Saunders Mac Lane Textbook 1978Latest edition Springer Science+Business Media New York 1978 Adjo
描述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 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 characterized 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 two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into
出版日期Textbook 1978Latest edition
關鍵詞Adjoint functor; Morphism; addition; algebra; theorem
版次2
doihttps://doi.org/10.1007/978-1-4757-4721-8
isbn_softcover978-1-4419-3123-8
isbn_ebook978-1-4757-4721-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1978
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沙發(fā)
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板凳
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Monads and Algebras, from this monad in .. Another principal result is a theorem due to Beck, which describes exactly those categories . with adjunctions 〈 ., ., .〉:.?. which can be so reconstructed from a monad . in the base category .. It then turns out that algebras in this last sense are so general as to include the compact Hausdorff spaces (§ 9).
地板
發(fā)表于 2025-3-22 08:33:39 | 只看該作者
Monoids,aces by this isomorphism. Closer analysis shows that more care is requisite in this identification — one must use the . isomorphism, and one must verify that the resulting identification of multiple products can be made in a “coherent” way.
5#
發(fā)表于 2025-3-22 08:47:56 | 只看該作者
0072-5285 s, 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 of the representations of functors by sets of morphisms, and a means of manipulating direct an
6#
發(fā)表于 2025-3-22 13:19:25 | 只看該作者
Organic Opals: Properties and Applicationsved. This leads to a set of axioms describing an “abelian” category. The axioms suffice to prove all the facts about commuting diagrams and connecting morphisms which are proved in Ab by methods of chasing elements. We carry the subject exactly to this point, leaving the subsequent development of homological algebra to more specialized treatments.
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8#
發(fā)表于 2025-3-22 23:50:42 | 只看該作者
Textbook 1978Latest editionok 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 of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse
9#
發(fā)表于 2025-3-23 05:22:51 | 只看該作者
Sabine W?hlke,Julia Inthorn,Silke Schicktanzersals and limits and examine a few basic types of limits (products, pullbacks, and equalizers ...). Deeper properties will appear in Chapter IX on special limits, while the relation to adjoints will be treated in Chapter V.
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