Complicial Sets Characterising The Simplicial Nerves Of Strict Omega Categories
Download Complicial Sets Characterising The Simplicial Nerves Of Strict Omega Categories PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Complicial Sets Characterising The Simplicial Nerves Of Strict Omega Categories book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories
Author: Dominic Verity
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
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.
Towards Higher Categories
Author: John C. Baez
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-09-24
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 itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Elements of ?-Category Theory
Author: Emily Riehl
language: en
Publisher: Cambridge University Press
Release Date: 2022-02-10
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.