Coherence In Three Dimensional Category Theory
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Coherence In Three Dimensional Category Theory
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Author : Nick Gurski
language : en
Publisher:
Release Date : 2013
Coherence In Three Dimensional Category Theory written by Nick Gurski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic book categories.
"In the study of higher categories, dimension three occupies an interesting position on the landscape of higher dimensional category theory. From the perspective of a "hands-on" approach to defining weak n-categories, tricategories represent the most complicated kind of higher category that the community at large seems comfortable working with."--
Coherence In Three Dimensional Category Theory
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Author : Nick Gurski
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-21
Coherence In Three Dimensional Category Theory written by Nick Gurski 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 2013-03-21 with Mathematics categories.
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
Coherence For Tricategories
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Author : Robert Gordon
language : en
Publisher:
Release Date : 1995
Coherence For Tricategories written by Robert Gordon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Homotopy theory categories.
Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation c. by Book News, Inc., Portland, Or.
2 Dimensional Categories
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Author : Niles Johnson
language : en
Publisher: Oxford University Press, USA
Release Date : 2021-01-31
2 Dimensional Categories written by Niles Johnson and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-31 with Mathematics categories.
2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Simplicial Methods For Higher Categories
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Author : Simona Paoli
language : en
Publisher: Springer
Release Date : 2019-06-03
Simplicial Methods For Higher Categories written by Simona Paoli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-03 with Mathematics categories.
This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.
Higher Dimensional Categories From Double To Multiple Categories
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Author : Grandis Marco
language : en
Publisher: World Scientific
Release Date : 2019-09-09
Higher Dimensional Categories From Double To Multiple Categories written by Grandis Marco 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.
Slenderness
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Author : Radoslav Dimitric
language : en
Publisher: Cambridge University Press
Release Date : 2019
Slenderness written by Radoslav Dimitric 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 2019 with Mathematics categories.
A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.
Auxiliary Polynomials In Number Theory
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Author : David Masser
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-21
Auxiliary Polynomials In Number Theory written by David Masser 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 2016-07-21 with Mathematics categories.
A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Canonical Ramsey Theory On Polish Spaces
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Author : Vladimir Kanovei
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-12
Canonical Ramsey Theory On Polish Spaces written by Vladimir Kanovei 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 2013-09-12 with Mathematics categories.
This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.
Fourier Integrals In Classical Analysis
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Author : Christopher D. Sogge
language : en
Publisher: Cambridge University Press
Release Date : 2017-04-27
Fourier Integrals In Classical Analysis written by Christopher D. Sogge 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 2017-04-27 with Mathematics categories.
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.