Monoidal Topology A Categorical Approach To Order Metric And Topology Encyclopedia Of Mathematics And Its Applications Free Books


THEORY AND APPLICATIONS OF CATEGORIES Volume 9, 2001-2
A Note On Actions Of A Monoidal Category G. Janelidze And G.M. Kelly 61 Classifying Spaces Of Categories And Term Rewriting Maurizio G. Citterio 92 Categorical Domain Theory: Scott Topology, Powercategories, Coherent Categories Panagis Karazeris 106 The Hurwitz Action And Braid Group Orderings Jonathon Funk 121 The Editors Of TAC Wish To Thank Aurelio Carboni, Pino Rosolini And Robert Walters ... 23th, 2020

Beyond AI: Interdisciplinary Aspects Of Arti?cial Intelligence
Fuzzy Sets And Systems 159, 77–80 (2008) 6. Esteva, F. And Godo, L.: Monoidal T-norm Based Logic: Towards A Logic For Left-continuous T-norms. Fuzzy Sets And Systems 124, 271–288 (2001) 7. Fodor, J.C.: A New Look At Fuzzy Connectives. Fuzzy Sets And Systems 57, 141– 148 (1993) 8. Fodor, J.C.: Contrapositive Symmetry Of Fuzzy Implications ... 10th, 2020

AN EXPLORATION OF
VEIT CATEGORY OF FINITE DIMENSIONAL IR VECTOR SPACES TENSOR PRODUCT A VECTOR Space OOCBASEVi.mg ITS DUAL Link OODYA.c.BAisyT V V Yin O Nzhm A O O V 0 Hi 9It Csu.it V. W NTe V Nine I Mi Imma I E I I F R O NE Etnn AEa E. OFTRACE EXTRA U ANAXIOMATISATION G I SYMMETRC MONOIDAL CATEGORY Nine Time Emma MONOIDAL ADD AN OPERATION ON ARROWS T.tw Turns Xx F U W V TraYuff U V O O Tru.uitlomluxou ... 3th, 2020

Advances In The Theory Of L Algebras - CiteSeerX
Advances In The Theory Of L Algebras 3 The Divisibility Condition Implies The Continuity Of The Monoidal Operation With Re-spect To The Order Topology: If Ais A BL Algebra, If X;Y Aand Inf Y And SupX Exists, Then For All A2A, Ainf Y = Inf(aY), And AsupX= Sup(aX). The Class Of BL Algebras Clearly Forms A Variety. Let :xbe An Abbreviation For X)0: 26th, 2020

New Techniques In Hopf Algebras And Graded Ring Theory
New Techniques In Hopf Algebras And Graded Ring Theory Koninklijke Vlaamse Academie Van Belgi¨e Voor Wetenschappen En Kunsten Vrije Universiteit Brussel September 19-23, 2006 Abstracts Alessandro Ardizzoni Weak Projections And Monoidal Categories Weak Projections Onto A Braided Bialgebra Are Produced By Means Of Hochschild Cohomology In The Framework Of Monoidal Categories. Thomas Aubriot On ... 1th, 2020

Pregroup Semantics In Compact Closed Monoidal Categories ...
Pregroup Semantics In Compact Closed Monoidal Categories With Biproducts Anne Preller LIRMM-CNRS, Montpellier, France Logic, Categories And Semantics Bordeaux, November 12-13, 2010 Bordeaux 2010, Preller@lirmm.fr Pregroup Semantics. Outlinesyntax + Semantics2-sorted Functionscompact Closed Categorysemantics In Compact Closed Categories Pregroup Grammar, A Compact Type-logical Grammar Syntactic ... 21th, 2020

Operads - Universiteit Utrecht
X8 Homology With Coef?cients . . . . . . . . . . . . . . . . . . . . 93 ... The Interplay Of Homotopy Theory On The Level Of Operads And Homotopy Theory At The Level Of Spaces With Algebraic Structure. Homological Algebra The Operad Axioms Can Directly Be Translated To Any Symmetric Monoidal Category (C;›;I). Above We Described The Situation For (C;›;I) = (Top;£;?), The Cate-gory Of ... 26th, 2020

ALGEBRAIC TOPOLOGICAL METHODS IN COMPUTER SCIENCE (ATMCS) III
ALGEBRAIC TOPOLOGICAL METHODS IN COMPUTER SCIENCE (ATMCS) III 7 Abstracts John Baez, Computations And The Periodic Table By Now There Is An Extensive Network Of Interlocking Analogies Between Physics, Topology, Logic And Computer Science, Which Can Be Seen Most Easily By Comparing The Roles That Symmetric Monoidal Closed Categories Play In Each Subject. However, Symmetric Monoidal Categories ... 4th, 2020

From Categories To Homotopy Theory Birgit Richter
Homology Of Iterated Loop Spaces 249 12.3.4. Stashe ’s Associahedra 250 12.4. E 1-monoidal Functors 254 7. CHAPTER 13. Classifying Spaces Of Symmetric Monoidal Categories 255 13.1. Commutative H-Space Structure On BCfor CSymmetric Monoidal 255 13.2. Group Completion Of Discrete Monoids 257 13.3. Grayson-Quillen Construction 259 13.4. Group Completion Of H-Spaces 262 CHAPTER 14. Approaches To ... 26th, 2020

Ronald Brown Ross Street March 1, 2011 ArXiv:1009.5609v2 ...
Determining A Maximal Tree In The Cayley Graph. Thus We See Covering Crossed Complexes As A Basic Tool In The Application Of Crossed Complex Methods, In Analogy To The Application Of Covering Spaces In Algebraic Topology. A Major Tool For Dealing With Homotopies Is The Construction Of A Monoidal Closed Structure On The Category Crsof Crossed Complexes Giving An Exponential Law Of The Form Crs ... 3th, 2020

Cocycle Twists And Extensions Of Braided Doubles Bazlov, Y ...
Cocycles, Central Extensions, The Schur Multiplier, Twisted Group Algebras 11 2. The Schur Multiplier Of S N 14 3. Cocycle Twists And Cocycle Extensions Of Group-graded Algebras 19 4. Cocycle Twists And The Lazy Cohomology Of A Monoidal Category 20 5. Cocycle Twists Of Braidings And Nichols Algebras 25 6. Extensions And Twists Of Yetter-Drinfeld Modules 31 7. Braided Doubles 38 8. Braided ... 3th, 2020

Ribbon Structure In Symmetric Pre-monoidal Categories
[5] Mac Lane S, 1998 Categories For The Working Mathematician 2nd. Ed. (Springer-Verlag, New York) [6] Isaac P S, Joyce W P And Links J, An Algebraic Origin For Quark Con?nement 2003 Preprint ArXiv:hep-th/0307046 [7] Altschuler D And Coste A, Quasi-quantum Groups, Knots, Three-manifolds And Topological ?eld Theory 1992 Commun. Math. Phys ... 6th, 2020

Stacks And Categories In Geometry, Topology, And Algebra ...
(differential, Topological Or Algebraic) Stack (or, In Particular, An Orbifold) Is V. Hinich, Drinfeld Double For Orbifolds, Contemporary Math. 433 Daniel Halpern-leistner - Columbia University Mathematical Interests: Algebraic Geometry, Derived Categories, Any Map Between Algebraic Stacks Yields A Symmetric Monoidal Functor Between Derived Cv - Mathematics - University Of Illinois At Thesis ... 11th, 2020

Network Theory I: Electrical Circuits And Signal-Flow ...
Network Theory I: Electrical Circuits And Signal-Flow Graphs John Baez, Jason Erbele, Brendan Fong. The Category With Vector Spaces As Objects And Linear Maps As Morphisms Becomes Symmetric Monoidal With The Usual . In Quantum Eld Theory, ‘Feynman Diagrams’ Are Pictures Of Morphisms In This Symmetric Monoidal Category: The Category With Vector Spaces As Objects And Linear Maps As Morphisms ... 20th, 2020

Notions Of Computation As Monoids (extended Version)
Applicative Functors, On The Other Hand, Are Usually Presented As Lax Monoidal Functors With A Compatible Strength [35, 28, 41]. However, In The Category-theory Community, It Is Known That Lax Monoidal Functors Are Monoids With Respect To The Day Convolution [14], And Hence Applicative Functors Are Also Monoids In A Monoidal Category Of Endofunctors Using The Day Convolution As A Tensor ... 5th, 2020

Notions Of Computation As Monoids ArXiv:1406.4823v1 [cs.LO ...
There Are Different Notions Of Computation, The Most Popular Being Monads, Applicative Functors, And Arrows. In This Article We Show That These Three Notions Can Be Seen As Monoids In A Monoidal Category. We Demonstrate That At This Level Of Abstraction One Can Obtain Useful Results Which Can Be Instantiated To The Different Notions Of Computation. In Particular, We Show How Free Constructions ... 1th, 2020

Tunisian Journal Of Mathematics - MSP
Tunisian Journal Of Mathematics An International Publication Organized By The Tunisian Mathematical Society Msp G-symmetric Monoidal Categories Of Modules Over Equivariant Commutative Ring Spectra Andrew J. Blumberg And Michael A. Hill 2020 Vol. 2 No. 2 4th, 2020

Double Construction For Monoidal Categories
Double Construction For Monoidal Categories CHRISTIAN KASSEL Universitd Louis Pasteur-C.N.R.S. Strasbourg, L~rance ... This Categorica ! Construction Is The Main Result Of This Paper. More Precisely, We Show How To Assign A Ribbon Category :D(C) To An Arbitrary M0noidal Category With Dual- Ity C. The Definition Of :D(C) Is An Elaboration Of The Definition Of The Centre Z(C): When C Is The ... 15th, 2020

Quantum CPOs - Act2020.mit.edu
A Suitable Monoidal Subcategory Representing Quantum Circuits, For Instance M := FdAlgop, The Opposite Of The Category Of Nite-dimensional Operator Algebras And Unital Y-homomorphisms. In [3], PQM Was Extended With Term Recursion, And In [4] The Circuit-free Fragment Of PQM Was Extended With Type Recursion. Furthermore, The Latter Article Also ... 15th, 2020

CHAPTER IV.3. FORMAL GROUPS AND LIE ALGEBRAS Contents
Co-algebras Associated To Formal Moduli Problems 7 1.2. The Monoidal Structure 10 1.3. The Functor Of Inf-spectrum 11 1.4. An Example: Vector Prestacks 13 2. Inf-a Neness 16 2.1. The Notion Of Inf-a Neness 16 2.2. Inf-a Neness And Inf-spectrum 17 2.3. A Criterion For Being Inf-a Ne 18 3. From Formal Groups To Lie Algebras 20 3.1. The Exponential Construction 20 3.2. Corollaries Of Theorem 3.1 ... 5th, 2020

The Direct Product Problem
Vipul Naik The Direct Product Cancellation Problem The Free Product Cancellation Problem Conclusions Monoidal Interpretation Consider A Commutative And Associative Monoid Whose: I Elements Are Isomorphism Classes Of Groups I Multiplication Map Is The Direct Product Operation. The Big Questions: I Which Elements Of The Monoid Are Cancellative? I Which Elements Of The Monoid Are Cancelductive ... 15th, 2020

THEORY AND APPLICATIONS OF CATEGORIES Volume 9, 2001-2
A Note On Actions Of A Monoidal Category G. Janelidze And G.M. Kelly 61 Classifying Spaces Of Categories And Term Rewriting Maurizio G. Citterio 92 Categorical Domain Theory: Scott Topology, Powercategories, Coherent Categories Panagis Karazeris 106 The Hurwitz Action And Braid Group Orderings Jonathon Funk 121 The Editors Of TAC Wish To Thank Aurelio Carboni, Pino Rosolini And Robert Walters ... 28th, 2020

ROBERT W. THOMASON, 1952-1995.
Paper Symmetric Monoidal Categories Model All Connective Spectra", Which Appeared In The Rst Volume Of Theory And Applications Of Categories, Thomason Returns To His Early Interests In In Nite Loop Space Machines, And Proves That The Well Known Construction Of A (-1)-connective Spectrum Out Of A Symmetric Monoidal Category Is A Localization" (i.e. Represents The Stable Homotopy Category Of ... 1th, 2020

Comparing Logics For Rewriting: Rewriting Logic, Action ...
Gs-monoidal Theories, Which Represent The Algebraic Counterpart Of Such Notions; They Give An Axiomatic Description To Various Graph-like Structures, Introducing Formalisms That Are Dierent From The Ordinary Tree-like Presentation Of Terms. We Often Use Such 21th, 2020

A Prehistory Of N-Categorical Physics
Eld Theory. In Parallel, We Trace A Bit Of The History Of N-categories, From Eilen-berg And Mac Lane’s Introduction Of Categories, To Later Work On Monoidal And Braided Monoidal Categories, To Grothendieck’s Dreams Involving 1-categories, And Subsequent Attempts To Realize This Dream. Our Chronology Ends At The Dawn Of The 21st Century; Since Then, Developments Have Been Coming So Thick ... 3th, 2020

Beyond AI: Interdisciplinary Aspects Of Arti?cial Intelligence
Fuzzy Sets And Systems 159, 77–80 (2008) 6. Esteva, F. And Godo, L.: Monoidal T-norm Based Logic: Towards A Logic For Left-continuous T-norms. Fuzzy Sets And Systems 124, 271–288 (2001) 7. Fodor, J.C.: A New Look At Fuzzy Connectives. Fuzzy Sets And Systems 57, 141– 148 (1993) 8. Fodor, J.C.: Contrapositive Symmetry Of Fuzzy Implications ... 9th, 2020

Reasoning With -Graphs
String Diagrams Provide An Intuitive Method For Reasoning About Monoidal Categories. However, This Does Not Negate The Ability For Those Using Them To Make Mistakes In Proofs. To This End, There Is A Project (Quantomatic) To Build A Proof Assistant For String Diagrams, At Least For Those Based On Categories With A Notion Of Trace. The Development 7th, 2020

Reasoning With -Graphs - Alex Merry
String Diagrams Provide An Intuitive Method For Reasoning About Monoidal Categories. However, This Does Not Negate The Ability For Those Using Them To Make Mistakes In Proofs. To This End, There Is A Project (Quantomatic) To Build A Proof Assistant For String Diagrams, At Least For Those Based On Categories With A Notion Of Trace. The Development 15th, 2020

FUNCTORIAL KNOT THEORY
4 Functorial Knot Theory II Deformations 11. Introduction 12. Definitions 13. Deformation Complexes Of Semigroupal Categories And Functors 14. Some Useful Cochain Maps 15. First Order Deformations 16. Obstructions And Cup Product And Pre-Lie Structures OnX*(F) 159 17. Units 175 18. Extrinsic Deformations Of Monoidal Categories 181 19. Vassiliev Invariants, Framed And Unframed 185 20. Vassiliev ... 13th, 2020

Rouquier Complexes Are Functorial Over Braid Cobordisms
SC And Knot Theory Have Come To Light. Originally Introduced By Soergel In [11], SC Is An Equivalent But More Combinatorial Description Of A Certain Category Of Harish-Chandra Modules Over A Semisimple Lie Algebra G. The Added Simplicity Of This Formulation Comes From The Fact That SC Is Just A Full Monoidal Subcategory Of Graded R-bimodules, Where R Is A Polynomial Ring Equipped With An ... 7th, 2020

Symmetric Monoidal Structure On Non-commutative Motives
Key Words: Non-commutative Motives, Non-commutative Algebraic Geom-etry, Non-connective Algebraic K-theory, Secondary K-theory, Hochschild Homology, Negative Cyclic Homology, Periodic Cyclic Homology Mathematics Subject Classi?cation 2000: 19D35, 19D55, 18D10, 18D20, 19E08 Contents 1 Preliminaries 208 2 Background On Dg Categories 210 3th, 2020

Introduction
On Free Yetter-Drinfeld Modules Over Adjoint Hopf Subalgebras And The Monoidal Invariance Of Gerstenhaber-Schack Cohomology, This Is Used To Show That Both Gerstenhaber-Schack And Hochschild Cohomological Dimensions Of The Coordinate Algebra Of The Quantum Permutation Group Are 3. 1. Introduction We Study Homological Properties Of Hopf Algebras By Using Yetter-Drinfeld Modules And Tensor ... 16th, 2020

FROBENIUS AND SEPARABLE FUNCTORS FOR THE CATEGORY OF ...
Entwined Modules Over Cowreaths In A Monoidal Category Are Introduced. They Can Be Identi Ed To Coalgebras In An Appropriate Monoidal Category. It Is Investigated When Such Coalgebras Are Frobenius (resp. Separable), And When The Forgetful Functor From Entwined Modules To Representations Of The Underlying Algebra Is Frobenius (resp. Separable). These Properties Are Equivalent When The Unit ... 19th, 2020

FROBENIUS AND SEPARABLE FUNCTORS FOR THE CATEGORY OF ...
Entwined Modules Over Cowreaths In A Monoidal Category Are Introduced. They Can Be Identi Ed To Coalgebras In An Appropriate Monoidal Category. It Is Investigated When Such Coalgebras Are Frobenius (resp. Separable), And When The Forgetful Functor From Entwined Modules To Representations Of The Underlying Algebra Is Frobenius (resp. Separable). These Properties Are Equivalent When The Unit ... 13th, 2020

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