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Pseudo Limits Biadjoints And Pseudo Algebras
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Book Synopsis Pseudo Limits, Biadjoints, and Pseudo Algebras by : Thomas M. Fiore
Download or read book Pseudo Limits, Biadjoints, and Pseudo Algebras written by Thomas M. Fiore and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pseudo Limits, Bi-adjoints, and Pseudo Algebras by : Thomas M. Fiore
Download or read book Pseudo Limits, Bi-adjoints, and Pseudo Algebras written by Thomas M. Fiore and published by . This book was released on 2005 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pseudo Limits, Biadjoints, and Pseudo Algebras: Categorical Foundations of Conformal Field Theory by : Thomas M. Fiore
Download or read book Pseudo Limits, Biadjoints, and Pseudo Algebras: Categorical Foundations of Conformal Field Theory written by Thomas M. Fiore and published by American Mathematical Soc.. This book was released on 2006 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg
Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Towards Higher Categories by : John C. Baez
Download or read book Towards Higher Categories written by John C. Baez and published by Springer Science & Business Media. This book was released on 2009-09-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebra and Coalgebra in Computer Science by : Alexander Kurz
Download or read book Algebra and Coalgebra in Computer Science written by Alexander Kurz and published by Springer Science & Business Media. This book was released on 2009-08-28 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semisolvability of Semisimple Hopf Algebras of Low Dimension by : Sonia Natale
Download or read book Semisolvability of Semisimple Hopf Algebras of Low Dimension written by Sonia Natale and published by American Mathematical Soc.. This book was released on 2007 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Hilbert Function of a Level Algebra by : A. V. Geramita
Download or read book The Hilbert Function of a Level Algebra written by A. V. Geramita and published by American Mathematical Soc.. This book was released on 2007 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Invariant Means and Finite Representation Theory of $C^*$-Algebras by : Nathanial Patrick Brown
Download or read book Invariant Means and Finite Representation Theory of $C^*$-Algebras written by Nathanial Patrick Brown and published by American Mathematical Soc.. This book was released on 2006 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 2-Dimensional Categories by : Niles Johnson
Download or read book 2-Dimensional Categories written by Niles Johnson and published by Oxford University Press, USA. This book was released on 2021-01-31 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Book Synopsis Homotopy Theory of Higher Categories by : Carlos Simpson
Download or read book Homotopy Theory of Higher Categories written by Carlos Simpson and published by Cambridge University Press. This book was released on 2011-10-20 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
Book Synopsis Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls by : Nicola Arcozzi
Download or read book Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls written by Nicola Arcozzi and published by American Mathematical Soc.. This book was released on 2006 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A tree structure for the unit ball $mathbb B? n$ in $mathbb C'n$; Carleson measures; Pointwise multipliers; Interpolating sequences; An almost invariant holomorphic derivative; Besov spaces on trees; Holomorphic Besov spaces on Bergman trees; Completing the multiplier interpolation loop; Appendix; Bibliography
Book Synopsis Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories by : Dominic Verity
Download or read book Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories written by Dominic Verity and published by American Mathematical Soc.. This book was released on 2008 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.
Book Synopsis Invariant Differential Operators for Quantum Symmetric Spaces by : Gail Letzter
Download or read book Invariant Differential Operators for Quantum Symmetric Spaces written by Gail Letzter and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Book Synopsis Torus Fibrations, Gerbes, and Duality by : Ron Donagi
Download or read book Torus Fibrations, Gerbes, and Duality written by Ron Donagi and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form
Book Synopsis Spinor Genera in Characteristic 2 by : Yuanhua Wang
Download or read book Spinor Genera in Characteristic 2 written by Yuanhua Wang and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to establish the spinor genus theory of quadratic forms over global function fields in characteristic 2. The first part of the paper computes the integral spinor norms and relative spinor norms. The second part of the paper gives a complete answer to the integral representations of one quadratic form by another with more than four variables over a global function field in characteristic 2.
Book Synopsis Exponential Genus Problems in One-Relator Products of Groups by : Andrew James Duncan
Download or read book Exponential Genus Problems in One-Relator Products of Groups written by Andrew James Duncan and published by American Mathematical Soc.. This book was released on 2007 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.
