**Author**: Benoit Fresse

**Publisher:**Springer Science & Business Media

**ISBN:**3540890556

**Category:**Mathematics

**Page:**308

**View:**8728

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

**Author**: Benoit Fresse

**Publisher:** Springer Science & Business Media

**ISBN:** 3540890556

**Category:** Mathematics

**Page:** 308

**View:** 8728

The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study 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:** 4116

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:** 1119

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:** 7942

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:** 5859

**Author**: Martin Markl

**Publisher:** American Mathematical Soc.

**ISBN:** 0821889796

**Category:** Mathematics

**Page:** 129

**View:** 3162

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.
*Proceedings of the International Conference on Operads and Universal Algebra, Tianjin, China, 5-9 July 2010*

**Author**: Chengming Bai,Li Guo,Jean-Louis Loday

**Publisher:** World Scientific

**ISBN:** 9814365114

**Category:** Mathematics

**Page:** 299

**View:** 709

The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.

**Author**: Gregory Arone,Michael Ching

**Publisher:** N.A

**ISBN:** 9782856293089

**Category:** Mathematics

**Page:** 158

**View:** 5011

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

**Publisher:** American Mathematical Soc.

**ISBN:** 1470421976

**Category:** Algebra, Homological

**Page:** 311

**View:** 2922

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

**Publisher:** American Mathematical Soc.

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 8032

*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:** 5763

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.
*The sciences and engineering*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Science

**Page:** N.A

**View:** 646

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

**Publisher:** American Mathematical Soc.

**ISBN:** 1470421976

**Category:** Algebra, Homological

**Page:** 311

**View:** 8452

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**: Dikran B. Karagueuzian

**Publisher:** N.A

**ISBN:** N.A

**Category:**

**Page:** 112

**View:** 6888

**Author**: Bodo Pareigis

**Publisher:** N.A

**ISBN:** N.A

**Category:** Categories (Mathematics)

**Page:** 192

**View:** 7100

**Author**: Michael Mürmann

**Publisher:** Springer-Verlag

**ISBN:** 364238160X

**Category:** Mathematics

**Page:** 428

**View:** 7469

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.

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