Simplicial Methods for Higher Categories : Segal-type Models of Weak n-Categories. 1st ed. 2019

種類:

電子ブック

責任表示:

by Simona Paoli

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Paoli, Simona.
• SpringerLink (Online service)

シリーズ名:

Algebra and Applications ; 26

ISBN:

9783030056742 [3030056740]    

注記:

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.
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-stand

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