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“…The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. …”
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“…This notion is studied from a) the homological point of view: construction of the (co)homology theory with trivial coefficients and general coefficients, b) the operadic point of view: determination of the dual operad, that is the dendriform dialgebras which are strongly related with the planar binary trees, c) the algebraic point of view: Hopf structure and Milnor-Moore type theorem.…”
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“…This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads. …”
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“…The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. …”
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“…The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory \operatorname{OpdBim}_{\mathcal{V}} of operad bimodules, that has operads as 0-cells, operad bimodules as 1-cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. …”
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“…The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. …”
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“…The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck-Teichmüller group from the viewpoint of the theory of operads. …”
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“…The ultimate goal of this book is to explain that the Grothendieck-Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. …”
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“…A convenient language for describing various structures arising naturally on topological spaces and on their cohomology and homotopy groups is the language of operads and algebras over an operad. This language was proposed by J. …”
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“…We share a small connection between information theory, algebra, and topology—namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their representations with topological simplices and the real line as the main example. …”
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“…In this paper, we argue that operads provide an effective knowledge representation to address these challenges. …”
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“…Finally, we give an operadic interpretation of the construction.…”
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