Complicial Sets Characterising the Simplicial Nerves of Strict [omega]-categories PDF Download

Complicial Sets Characterising the Simplicial Nerves of Strict [omega]-categories PDF
By:Dominic Verity
Published on 2008-04-03 by American Mathematical Soc.

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.

This Book was ranked at 40 by Google Books for keyword mathematics about sets.

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Book which was published by American Mathematical Soc. since 2008-04-03 have ISBNs, ISBN 13 Code is 9780821866467 and ISBN 10 Code is 082186646X

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