**Author**: Benoit Fresse

**Publisher:**Springer

**ISBN:**3540890564

**Category:**Mathematics

**Page:**314

**View:**8819

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# Search Results for: modules-over-operads-and-functors

**Author**: Benoit Fresse

**Publisher:** Springer

**ISBN:** 3540890564

**Category:** Mathematics

**Page:** 314

**View:** 8819

This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

**Author**: Nicola Gambino,André Joyal

**Publisher:** American Mathematical Soc.

**ISBN:** 1470425769

**Category:** Algebra, Homological

**Page:** 110

**View:** 8881

The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.

**Author**: Christian Ausoni,Kathryn Hess,Brenda Johnson,Wolfgang Lück,Jérôme Scherer

**Publisher:** American Mathematical Soc.

**ISBN:** 0821891456

**Category:** Mathematics

**Page:** 296

**View:** 9500

This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
*14th International Workshop, WoLLIC 2007, Rio de Janeiro, Brazil, July 2-5, 2007, Proceedings*

**Author**: Daniel Leivant,Ruy de Queiroz

**Publisher:** Springer

**ISBN:** 3540734457

**Category:** Computers

**Page:** 366

**View:** 5098

The 14th International Workshop on Logic, Language, Information and Computation focused on foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions, and resources; and foundational aspects of information organization, search, flow, sharing, and protection.

**Author**: Arthur James Wells

**Publisher:** N.A

**ISBN:** N.A

**Category:** English literature

**Page:** N.A

**View:** 2088

**Author**: Thomas Schuster

**Publisher:** Springer Science & Business Media

**ISBN:** 3540712267

**Category:** Mathematics

**Page:** 198

**View:** 6322

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.

**Author**: Bernard Roynette,Marc Yor

**Publisher:** Springer Science & Business Media

**ISBN:** 3540896988

**Category:** Mathematics

**Page:** 275

**View:** 1879

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder 40] and Laumon 62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in 115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan's conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.

**Author**: Martin Markl

**Publisher:** American Mathematical Soc.

**ISBN:** 0821889796

**Category:** Mathematics

**Page:** 129

**View:** 1787

This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.

**Author**: Donald Yau, Mark W. Johnson

**Publisher:** American Mathematical Soc.

**ISBN:** 1470421976

**Category:** Algebra, Homological

**Page:** 311

**View:** 8677

PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.

**Author**: Werner Ballmann

**Publisher:** Springer-Verlag

**ISBN:** 3034809018

**Category:** Mathematics

**Page:** 162

**View:** 5769

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

**Author**: Emil Artin

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** 560

**View:** 5189

**Author**: Donald Yau, Mark W. Johnson

**Publisher:** American Mathematical Soc.

**ISBN:** 1470421976

**Category:** Algebra, Homological

**Page:** 311

**View:** 9712

PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.

**Author**: Bodo Pareigis

**Publisher:** N.A

**ISBN:** N.A

**Category:** Categories (Mathematics)

**Page:** 192

**View:** 9231

**Author**: Peter Gabriel,Friedrich Ulmer

**Publisher:** Springer-Verlag

**ISBN:** 3540368868

**Category:** Mathematics

**Page:** 200

**View:** 6129

*Lateinisch-Deutsch*

**Author**: Gottfried W Leibniz,Franz Schupp

**Publisher:** N.A

**ISBN:** 3787332537

**Category:** Philosophy

**Page:** 266

**View:** 6529

Die Generales Inquisitiones von 1686 stellen die wichtigste geschlossene Arbeit Leibniz' zu Fragen der Logik dar. Wie in dem ebenfalls 1686 verfaßten Discours de Métaphysique (PhB 260) wird hier Leibniz' Auffassung deutlich, in seinem Denken eine gewisse systematische Geschlossenheit gefunden zu haben.

**Author**: Donald G. Babbitt,Jane E. Kister

**Publisher:** American Mathematical Soc.

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 1386

*Proceedings of Renaissance Conferences*

**Author**: Jean-Louis Loday,James D. Stasheff,Alexander A. Voronov

**Publisher:** American Mathematical Soc.

**ISBN:** 0821805134

**Category:** Mathematics

**Page:** 443

**View:** 4667

Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory.

**Author**: Yuliya Mishura

**Publisher:** Springer Science & Business Media

**ISBN:** 3540758720

**Category:** Mathematics

**Page:** 393

**View:** 6059

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder 40] and Laumon 62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in 115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan's conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.

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