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Titlebook: Hopf Algebras and Their Generalizations from a Category Theoretical Point of View; Gabriella B?hm Book 2018 Springer Nature Switzerland AG

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發(fā)表于 2025-3-21 18:28:44 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
編輯Gabriella B?hm
視頻videohttp://file.papertrans.cn/429/428246/428246.mp4
概述First book to provide a unified category theoretical description of apparently different generalizations of Hopf algebras (including Hopf algebroids, weak Hopf algebras, and Hopf bimonoids in duoidal
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Hopf Algebras and Their Generalizations from a Category Theoretical Point of View;  Gabriella B?hm Book 2018 Springer Nature Switzerland AG
描述.These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications..Since Sweedler‘s work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, se
出版日期Book 2018
關(guān)鍵詞MSC (2010): 16T10, 16T05, 18C15, 18D10, 18D15; bialgebra; Hopf algebra; bialgebroid; Hopf algebroid; weak
版次1
doihttps://doi.org/10.1007/978-3-319-98137-6
isbn_softcover978-3-319-98136-9
isbn_ebook978-3-319-98137-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer Nature Switzerland AG 2018
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Solutions to the Exercises,This chapter presents fully worked solutions to the exercises in the previous chapters of this book.
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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View978-3-319-98137-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
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發(fā)表于 2025-3-22 18:10:15 | 只看該作者
ed, the aircraft’s trajectory must be planned carefully and optimized as there are inevitable remaining risks which should be minimized when flying over sparsely populated areas. The risk may be mitigated by a safe termination of the flight if circumstances permit. Also, the probability of violating
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發(fā)表于 2025-3-22 23:56:32 | 只看該作者
Gabriella B?hmed, the aircraft’s trajectory must be planned carefully and optimized as there are inevitable remaining risks which should be minimized when flying over sparsely populated areas. The risk may be mitigated by a safe termination of the flight if circumstances permit. Also, the probability of violating
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發(fā)表于 2025-3-23 05:26:33 | 只看該作者
Gabriella B?hmhe shelf by non-experts. To be effective in practice, such systems need to automatically choose a good algorithm and feature preprocessing steps for a new dataset at hand, and also set their respective hyperparameters. Recent work has started to tackle this . problem with the help of efficient Bayes
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發(fā)表于 2025-3-23 07:30:02 | 只看該作者
Gabriella B?hmauthor who produced most of the numerical analyses and plots.) (NIPS 2015 – ICML 2016) consisted of six rounds of a machine learning competition of progressive difficulty, subject to limited computational resources. It was followed bya one-round AutoML challenge (PAKDD 2018). The AutoML setting diff
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