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Titlebook: An Invitation to General Algebra and Universal Constructions; George M. Bergman Textbook 2015Latest edition Springer International Publish

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樓主
發(fā)表于 2025-3-21 19:29:18 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱An Invitation to General Algebra and Universal Constructions
影響因子2023George M. Bergman
視頻videohttp://file.papertrans.cn/156/155636/155636.mp4
發(fā)行地址Reviews many concrete examples of universal constructions, motivating the development of general algebra and the category-theoretic view of universal constructions.Enriches the reader‘s intuition of t
學(xué)科分類Universitext
圖書封面Titlebook: An Invitation to General Algebra and Universal Constructions;  George M. Bergman Textbook 2015Latest edition Springer International Publish
影響因子.Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader‘s grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book..
Pindex Textbook 2015Latest edition
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沙發(fā)
發(fā)表于 2025-3-22 00:12:01 | 只看該作者
Categories and Functorsthe category of all sets is handled using Grothendieck’s Axiom of Universes. Epimorphisms, monomorphisms, and similar concepts are investigated. The concept of “enriched categories” (for example, additive categories) is briefly sketched.
板凳
發(fā)表于 2025-3-22 03:20:57 | 只看該作者
https://doi.org/10.1007/978-3-319-11478-1Galois connections; categories; functors; coalgebra objects; free groups; lattices; ordered sets; universa
地板
發(fā)表于 2025-3-22 07:10:19 | 只看該作者
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發(fā)表于 2025-3-22 12:00:50 | 只看該作者
An Invitation to General Algebra and Universal Constructions978-3-319-11478-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
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發(fā)表于 2025-3-22 14:10:07 | 只看該作者
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發(fā)表于 2025-3-22 17:47:43 | 只看該作者
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發(fā)表于 2025-3-23 01:05:36 | 只看該作者
,Die Messung der Produktivit?t, studied include groups presented by generators and relations, Burnside groups, products and coproducts of groups (leading to the contrast between left and right universal constructions), similar constructions for monoids, rings, and Boolean rings, and constructions connecting one sort of structure
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發(fā)表于 2025-3-23 05:10:41 | 只看該作者
Sarah Henneberger-Sudjana,Fred Hennebergerescending chain condition is formalized. The axioms of Zermelo–Fraenkel Set Theory with Choice, and the arithmetic of ordinals and cardinals, are reviewed, and Zorn’s Lemma is developed. We end with some thoughts on whether set theory is “real”.
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發(fā)表于 2025-3-23 07:53:59 | 只看該作者
Die informatisierte Service-?konomieound, and as algebraic structures, and various completeness conditions they can satisfy are examined.Such structures often arise from . on sets, and this concept is developed.An insufficiently well known source of closure operators, which we develop, is the concept of a . between two sets. In the ca
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