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Simplicial methods for higher categories : segal-type models of weak n-categories

Author: Simona Paoli
Publisher: Cham : Springer, 2019.
Series: Algebras and applications.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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.
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Simona Paoli
ISBN: 9783030056742 3030056740 3030056732 9783030056735 9783030056759 3030056759
OCLC Number: 1103605872
Description: 1 online resource.
Contents: Part I --
Higher Categories: Introduction and Background --
An Introduction to Higher Categories --
Multi-simplicial techniques --
An Introduction to the three Segal-type models --
Techniques from 2-category theory --
Part II --
The Three Segal-Type Models and Segalic Pseudo-Functors --
Homotopically discrete n-fold categories --
The Definition of the three Segal-type models --
Properties of the Segal-type models --
Pseudo-functors modelling higher structures --
Part III --
Rigidification of Weakly Globular Tamsamani n-Categories by Simpler Ones --
Rigidifying weakly globular Tamsamani n-categories --
Part IV. Weakly globular n-fold categories as a model of weak n-categories --
Functoriality of homotopically discrete objects --
Weakly Globular n-Fold Categories as a Model of Weak n-Categories --
Conclusions and further directions --
A Proof of Lemma 0.1.4 --
References --
Index.
Series Title: Algebras and applications.
Responsibility: Simona Paoli.

Abstract:

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.

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