Coherence In Three Dimensional Category Theory PDF Download
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Author | : Nick Gurski |
Publisher | : |
Total Pages | : 288 |
Release | : 2014-05-14 |
Genre | : Tricategories |
ISBN | : 9781107336896 |
Download Coherence in Three-Dimensional Category Theory Book in PDF, ePub and Kindle
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
Author | : Nick Gurski |
Publisher | : Cambridge University Press |
Total Pages | : 287 |
Release | : 2013-03-21 |
Genre | : Mathematics |
ISBN | : 1107034892 |
Download Coherence in Three-Dimensional Category Theory Book in PDF, ePub and Kindle
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
Author | : Nick Gurski |
Publisher | : Cambridge University Press |
Total Pages | : 286 |
Release | : 2013-03-21 |
Genre | : Mathematics |
ISBN | : 9781107034891 |
Download Coherence in Three-Dimensional Category Theory Book in PDF, ePub and Kindle
Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.
Author | : Robert Gordon |
Publisher | : American Mathematical Soc. |
Total Pages | : 96 |
Release | : 1995-09-28 |
Genre | : Mathematics |
ISBN | : 9780821862810 |
Download Coherence for Tricategories Book in PDF, ePub and Kindle
The need to address the appropriate three-dimensional generalization of category (tricategory) has been felt in homotopy theory, low-dimensional topology, cohomology theory, category theory, and quantum field theory. Benabou's bicategories provide the two-dimensional notion into which examples naturally fit. In developing the theory of bicategories it is very reassuring to know the coherence theorem: They can be replaced by the stricter 2-categories which are merely categories enriched in the category of categories. In this book, the authors provide ... the unique source of the full definition of tricategory a thorough and complete proof of the coherence theorem for tricategories a wholly modern source of material on Gray's tensor product of 2-categories
Author | : Niles Johnson |
Publisher | : Oxford University Press, USA |
Total Pages | : 636 |
Release | : 2021-01-31 |
Genre | : Mathematics |
ISBN | : 0198871376 |
Download 2-Dimensional Categories Book in PDF, ePub and Kindle
2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Author | : Simona Paoli |
Publisher | : Springer |
Total Pages | : 343 |
Release | : 2019-06-03 |
Genre | : Mathematics |
ISBN | : 3030056740 |
Download Simplicial Methods for Higher Categories Book in PDF, ePub and Kindle
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.
Author | : Radoslav Dimitric |
Publisher | : Cambridge University Press |
Total Pages | : 330 |
Release | : 2019 |
Genre | : Mathematics |
ISBN | : 110847442X |
Download Slenderness Book in PDF, ePub and Kindle
A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.
Author | : Robert Gordon |
Publisher | : American Mathematical Soc. |
Total Pages | : 94 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 0821803441 |
Download Coherence for Tricategories Book in PDF, ePub and Kindle
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.
Author | : Tom Leinster |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1107044243 |
Download Basic Category Theory Book in PDF, ePub and Kindle
A short introduction ideal for students learning category theory for the first time.
Author | : Emily Riehl |
Publisher | : Cambridge University Press |
Total Pages | : 782 |
Release | : 2022-02-10 |
Genre | : Mathematics |
ISBN | : 1108952194 |
Download Elements of ∞-Category Theory Book in PDF, ePub and Kindle
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.