Author: Nick Gurski
Publisher:
ISBN: 9781107336896
Category : Tricategories
Languages : en
Pages : 288

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Book Description
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
ISBN: 1107034892
Category : Mathematics
Languages : en
Pages : 287

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Book Description
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
ISBN: 9781107034891
Category : Mathematics
Languages : en
Pages : 286

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Book Description
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.
ISBN: 9780821862810
Category : Mathematics
Languages : en
Pages : 96

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Book Description
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
ISBN: 0198871376
Category : Mathematics
Languages : en
Pages : 636

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Book Description
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
ISBN: 3030056740
Category : Mathematics
Languages : en
Pages : 343

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Book Description
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: Robert Gordon
Publisher: American Mathematical Soc.
ISBN: 0821803441
Category : Mathematics
Languages : en
Pages : 94

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Book Description
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: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273

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Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author: Radoslav Milan Dimitric
Publisher: Cambridge University Press
ISBN: 110847442X
Category : Mathematics
Languages : en
Pages : 330

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Book Description
A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.

Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193

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Book Description
A short introduction ideal for students learning category theory for the first time.