Dear Colleagues, As promised many years ago, I have finally committed my proof of the "Street-Roberts" conjecture to paper. This work demonstrates that Ross Street's simplicial nerve construction provides an equivalence between the category of (strict) \omega-categories and John Roberts' category of complicial sets. A draft of this work should appear on the arXiv.org e-print sometime in the next 24 hours, but in the meantime it may be downloaded as a PDF file from http://vesuvius.ics.mq.edu.au/~domv/complicialsets.pdf Regards Dom ------------------------------------------------ A/Prof. Dominic Verity Academic Director PPDP Division of ICS Macquarie University ------------------------------------------------------------------------ ------ \\ Title: Complicial Sets Authors: Dominic Verity Comments: 129 pages Subj-class: Category Theory; Algebraic Topology MSC-class: 18D05, 55U10 (Primary) 18D15, 18D20, 18D35, 18F99, 18G30 (Secondary) \\ The primary purpose of this work is to characterise strict \omega-categories as simplicial sets with structure. We prove the Street-Roberts conjecture which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title. \\ ------------------------------------------------------------------------ ------ 19-Oct-2004 17:24:01 -0300,3590;000000000000-00000000