Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories

Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories
Author :
Publisher : American Mathematical Soc.
Total Pages : 208
Release :
ISBN-10 : 9780821841426
ISBN-13 : 0821841424
Rating : 4/5 (424 Downloads)

Book Synopsis Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories by : Dominic Verity

Download or read book Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories written by Dominic Verity and published by American Mathematical Soc.. This book was released on 2008 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.

Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories Related Books

Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories
Language: en
Pages: 208
Authors: Dominic Verity
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

GET EBOOK

The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjectur
Towards Higher Categories
Language: en
Pages: 292
Authors: John C. Baez
Categories: Algebra
Type: BOOK - Published: 2009-09-24 - Publisher: Springer Science & Business Media

GET EBOOK

The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory
Diagrammatic Morphisms and Applications
Language: en
Pages: 232
Authors: David E. Radford
Categories: Mathematics
Type: BOOK - Published: 2003 - Publisher: American Mathematical Soc.

GET EBOOK

The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely us
Deep Beauty
Language: en
Pages: 487
Authors: Hans Halvorson
Categories: Mathematics
Type: BOOK - Published: 2011-04-18 - Publisher: Cambridge University Press

GET EBOOK

No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory ma
Elements of ∞-Category Theory
Language: en
Pages: 782
Authors: Emily Riehl
Categories: Mathematics
Type: BOOK - Published: 2022-02-10 - Publisher: Cambridge University Press

GET EBOOK

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninit