Complicial sets characterising the simplical nerves of strict ω-categories
Author(s)
Bibliographic Information
Complicial sets characterising the simplical nerves of strict ω-categories
（Memoirs of the American Mathematical Society, no. 905）
American Mathematical Society, 2008
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Note
Includes bibliographical references (p. 173-174) and indexes
Description and Table of Contents
Description
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).
Table of Contents
Simplicial operators and simplicial sets A little categorical background Double categories, 2-categories and $n$-categories An introduction to the decalage construction Stratifications and filterings of simplicial sets Pre-complicial sets Complicial sets The path category construction Complicial decalage constructions Street's $\omega$-categorical nerve construction Bibliography.
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