### Abstract

Language | English |
---|---|

Place of Publication | Providence, RI |

Publisher | American Mathematical Society |

ISBN (Print) | 9780821841426 |

Publication status | Published - 2008 |

### Publication series

Name | Memoirs of the American Mathematical Society |
---|---|

Publisher | American Mathematical Society |

No. | 905 |

ISSN (Print) | 0065-9266 |

### Fingerprint

### Keywords

- Categories (Mathematics)
- Algebraic topology

### Cite this

*Complicial sets characterising the simplicial nerves of strict ω-categories*. (Memoirs of the American Mathematical Society; No. 905). Providence, RI: American Mathematical Society.

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*Complicial sets characterising the simplicial nerves of strict ω-categories*. Memoirs of the American Mathematical Society, no. 905, American Mathematical Society, Providence, RI.

**Complicial sets characterising the simplicial nerves of strict ω-categories.** / Verity, Dominic.

Research output: Book/Report › Book › Research › peer-review

TY - BOOK

T1 - Complicial sets characterising the simplicial nerves of strict ω-categories

AU - Verity, Dominic

PY - 2008

Y1 - 2008

N2 - The primary purpose of this work is to characterise strict ω-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 ω-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.

AB - The primary purpose of this work is to characterise strict ω-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 ω-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.

KW - Categories (Mathematics)

KW - Algebraic topology

M3 - Book

SN - 9780821841426

T3 - Memoirs of the American Mathematical Society

BT - Complicial sets characterising the simplicial nerves of strict ω-categories

PB - American Mathematical Society

CY - Providence, RI

ER -