Formal Category Theory Adjointness For 2 Categories
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Formal Category Theory Adjointness For 2 Categories
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Author : John Walker Gray
language : en
Publisher: Springer Verlag
Release Date : 1974
Formal Category Theory Adjointness For 2 Categories written by John Walker Gray and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Formal Category Theory Adjointness For 2 Categories
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Author : J.W. Gray
language : en
Publisher: Springer
Release Date : 2006-11-15
Formal Category Theory Adjointness For 2 Categories written by J.W. Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Formal Category Theory
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Author : John W. Gray
language : en
Publisher:
Release Date : 1974
Formal Category Theory written by John W. Gray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Categories (Mathematics) categories.
Formal Category Theory
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Author : J. W. Gray
language : en
Publisher:
Release Date : 2014-09-01
Formal Category Theory written by J. W. Gray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Formal Category Theory
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Author : John Walker Gray
language : en
Publisher:
Release Date : 1974
Formal Category Theory written by John Walker Gray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Categories (Mathematics) categories.
Higher Dimensional Categories From Double To Multiple Categories
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2019-09-09
Higher Dimensional Categories From Double To Multiple Categories written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions.We want to show the advantages of this form for the theory of adjunctions and limits. Furthermore, this form is much simpler in higher dimension, starting with dimension three where weak 3-categories (also called tricategories) are already quite complicated, much more than weak or lax triple categories.This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories.
Handbook Of Categorical Algebra Basic Category Theory
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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 1994
Handbook Of Categorical Algebra Basic Category Theory written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The first of a 3-volume work, this text gives a detailed account of what should be known by all working in, or using category theory. This volume covers basic the concepts.
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.
Mathematical Applications Of Category Theory
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Author : American Mathematical Society. Meeting
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Mathematical Applications Of Category Theory written by American Mathematical Society. Meeting 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 1984 with Mathematics categories.
Contains the proceedings of the AMS Summer Research Conference on Axiomatic Set Theory, held in Boulder, Colorado, June 19-25, 1983. This work covers the various areas of set theory, including constructibility, forcing, combinatorics and descriptive set theory.
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.