Coherence For Tricategories
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Coherence For Tricategories
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Author : Robert Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Coherence For Tricategories written by Robert Gordon 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 1995 with Mathematics categories.
This work defines the concept of tricategory as the natural 3-dimensional generalization of bicategory. Trihomomorphism and triequivalence for tricategories are also defined so as to extend the concepts of homomorphism and biequivalence for bicategories.
Coherence In Three Dimensional Category Theory
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Author : Nick Gurski
language : en
Publisher:
Release Date : 2014-05-14
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 2014-05-14 with Tricategories categories.
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
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.
2 Dimensional Categories
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Author : Niles Johnson
language : en
Publisher: Oxford University Press
Release Date : 2021-01-31
2 Dimensional Categories written by Niles Johnson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-31 with Science 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.
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.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2012-12-06 with Mathematics categories.
This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Why Tricategories
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Author : A. J. Power
language : en
Publisher:
Release Date : 1994
Why Tricategories written by A. J. Power and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Categories (Mathematics) categories.
Hopf Algebras Quantum Groups And Yang Baxter Equations
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Author : Florin Felix Nichita
language : en
Publisher: MDPI
Release Date : 2019-01-31
Hopf Algebras Quantum Groups And Yang Baxter Equations written by Florin Felix Nichita and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-31 with Mathematics categories.
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
Homotopy Theory Of Higher Categories
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Author : Carlos Simpson
language : en
Publisher: Cambridge University Press
Release Date : 2011-10-20
Homotopy Theory Of Higher Categories written by Carlos Simpson 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 2011-10-20 with Mathematics categories.
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.
The Homotopy Theory Of 1 Categories
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Author : Julia E. Bergner
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-15
The Homotopy Theory Of 1 Categories written by Julia E. Bergner 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 2018-03-15 with Mathematics categories.
An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.