Simplicial Methods for Higher Categories Segal-type Models of Weak n-Categories /

• Κύριος συγγραφέας: Paoli, Simona (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Algebra and Applications, 26
• Θέματα: Category theory (Mathematics).; Homological algebra.; Algebraic topology.; Mathematical physics.; Algebraic geometry.; Category Theory, Homological Algebra.; Algebraic Topology.; Mathematical Physics.; Algebraic Geometry.

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...

Πίνακας περιεχομένων:

• 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.