Simplicial Methods for Higher Categories Segal-type Models of Weak n-Categories / by Simona Paoli.

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 t...

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Bibliographic Details
Main Author:	Paoli, Simona (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Cham : Springer International Publishing : Imprint: Springer, 2019.
Edition:	1st ed. 2019.
Series:	Algebra and Applications, 26 Springer eBook Collection.
Subjects:	Category theory (Mathematics). Homological algebra. Algebraic topology. Mathematical physics. Algebraic geometry. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

Table of 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.

Simplicial Methods for Higher Categories Segal-type Models of Weak n-Categories / by Simona Paoli.

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