Pseudo Limits Biadjoints And Pseudo Algebras
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Pseudo Limits Biadjoints And Pseudo Algebras
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Author : Thomas M. Fiore
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Pseudo Limits Biadjoints And Pseudo Algebras written by Thomas M. Fiore and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with MATHEMATICS categories.
In this paper, we develop the categorical foundations needed for working out completely the rigorous approach to the definition of conformal field theory outlined by Graeme Segal. We discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits, bicolimits, biadjoints, stacks, and related concepts. These 2-categorical concepts are used to describe the algebraic structure on the class of rigged surfaces. A rigged surface is a real, compact, not necessarily connected, two dimensional manifold with complex structure and analytically parametrized boundary components. This class admits algebraic operations of disjoint union and gluing as well as a unit. These operations satisfy axioms such as unitality and distributivity up to coherence isomorphisms which satisfy coherence diagrams. These operations, coherences, and their diagrams are neatly encoded as a pseudo algebra over the 2-theory of commutative monoids with cancellation.
Pseudo Limits Biadjoints And Pseudo Algebras Categorical Foundations Of Conformal Field Theory
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Author : Thomas M. Fiore
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Pseudo Limits Biadjoints And Pseudo Algebras Categorical Foundations Of Conformal Field Theory written by Thomas M. Fiore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In this paper we develop the categorical foundations needed for working out completely the rigorous approach to the definition of conformal field theory outlined by Graeme Segal. We discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits, bicolimits, biadjoints, stacks, and related concepts. These 2-categorical concepts are used to describe the algebraic structure on the class of rigged surfaces. A rigged surface is a real, compact, not necessarilyconnected, two dimensional manifold with complex structure and analytically parametrized boundary components. This class admits algebraic operations of disjoint union and gluing as well as a unit. These operations satisfy axioms such as unitality and distributivity up to coherence isomorphisms whichsatisfy coherence diagrams. These operations, coherences, and their diagrams are neatly encoded as a pseudo algebra over the 2-theory of commutative monoids with cancellation. A conformal field theory is a morphism of stacks of such structures. This paper begins with a review of 2-categorical concepts, Lawvere theories, and algebras over Lawvere theories. We prove that the 2-category of small pseudo algebras over a theory admits weighted pseudo limits and weighted bicolimits. This 2-category isbiequivalent to the 2-category of algebras over a 2-monad with pseudo morphisms. We prove that a pseudo functor admits a left biadjoint if and only if it admits certain biuniversal arrows. An application of this theorem implies that the forgetful 2-functor for pseudo algebras admits a leftbiadjoint. We introduce stacks for Grothendieck topologies and prove that the traditional definition of stacks in terms of descent data is equivalent to our definition via bilimits. The paper ends with a proof that the 2-category of pseudo algebras over a 2-theory admits weighted pseudo limits. This result is relevant to the definition of conformal field theory because bilimits are necessary to speak of stacks.
Pseudo Limits Bi Adjoints And Pseudo Algebras
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Author : Thomas M. Fiore
language : en
Publisher:
Release Date : 2005
Pseudo Limits Bi Adjoints And Pseudo Algebras written by Thomas M. Fiore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Limit Theorems Of Polynomial Approximation With Exponential Weights
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Author : Michael I. Ganzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Limit Theorems Of Polynomial Approximation With Exponential Weights written by Michael I. Ganzburg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.
Towards Higher Categories
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Author : John C. Baez
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-23
Towards Higher Categories written by John C. Baez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-23 with Mathematics categories.
This IMA Volume in Mathematics and its Applications TOWARDS HIGHER CATEGORIES contains expository and research papers based on a highly successful IMA Summer Program on n-Categories: Foundations and Applications. We are grateful to all the participants for making this occasion a very productive and stimulating one. We would like to thank John C. Baez (Department of Mathematics, University of California Riverside) and J. Peter May (Department of Ma- ematics, University of Chicago) for their superb role as summer program organizers and editors of this volume. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Fadil Santosa, Director of the IMA Markus Keel, Deputy Director of the IMA v PREFACE DEDICATED TO MAX KELLY, JUNE 5 1930 TO JANUARY 26 2007. This is not a proceedings of the 2004 conference “n-Categories: Fo- dations and Applications” that we organized and ran at the IMA during the two weeks June 7–18, 2004! We thank all the participants for helping make that a vibrant and inspiring occasion. We also thank the IMA sta? for a magni?cent job. There has been a great deal of work in higher c- egory theory since then, but we still feel that it is not yet time to o?er a volume devoted to the main topic of the conference.
Algebra And Coalgebra In Computer Science
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Author : Alexander Kurz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-28
Algebra And Coalgebra In Computer Science written by Alexander Kurz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-28 with Computers categories.
This book constitutes the proceedings of the Third International Conference on Algebra and Coalgebra in Computer Science, CALCO 2009, formed in 2005 by joining CMCS and WADT. This year the conference was held in Udine, Italy, September 7-10, 2009. The 23 full papers were carefully reviewed and selected from 42 submissions. They are presented together with four invited talks and workshop papers from the CALCO-tools Workshop. The conference was divided into the following sessions: algebraic effects and recursive equations, theory of coalgebra, coinduction, bisimulation, stone duality, game theory, graph transformation, and software development techniques.
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension
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Author : Sonia Natale
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension written by Sonia Natale and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
The Hilbert Function Of A Level Algebra
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Author : A. V. Geramita
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Hilbert Function Of A Level Algebra written by A. V. Geramita and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values.
Invariant Means And Finite Representation Theory Of C Algebras
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Author : Nathanial Patrick Brown
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Invariant Means And Finite Representation Theory Of C Algebras written by Nathanial Patrick Brown and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Various subsets of the tracial state space of a unital C$*$-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II$ 1$-factor representations of a class of C$*$-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II$ 1$-factor representations. In addition to developing some general theory we also show that these ideas are related to numerous other problems inoperator algebras.
2 Dimensional Categories
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Author : Niles Johnson
language : en
Publisher: Oxford University Press (UK)
Release Date : 2021
2 Dimensional Categories written by Niles Johnson and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Computers categories.
Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac Lane. It describes relationships between mathematical structures. Outside of pure mathematics, category theory is an important tool in physics, computer science, linguistics, and a quickly-growing list of other sciences. This book is about 2-dimensional categories, which add an extra dimension of richness and complexity to category theory. 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax functors, 2-/bilimits, the Duskin nerve, 2-nerve, internal adjunctions, monads in bicategories, 2-monads, biequivalences, the Bicategorical Yoneda Lemma, and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.