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**The combinatorics of n-categorical pasting.**
*(English)*
Zbl 0694.18007

Pasting 2-cells in a diagram is a somehow obvious process on any simple concrete example you have in mind. When the diagram gets complicated and various horizontal and vertical compositions are mixed, you rapidly give up and write “One proves easily that this defines a composite cell...” Amazingly enough, the metatheorem everybody had in mind about pasting 2- cells was never proved before this paper, even if the attempts to do so were numerous.

The present paper should therefore be considered as a central one in 2- category theory and even, more generally, in n-category theory, since this is the context in which the pasting theorem is proved. The paper is moreover very nicely written. It should be read by anybody using 2- categories.

The present paper should therefore be considered as a central one in 2- category theory and even, more generally, in n-category theory, since this is the context in which the pasting theorem is proved. The paper is moreover very nicely written. It should be read by anybody using 2- categories.

Reviewer: F.Borceux

### MSC:

18D05 | Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) |

### References:

[1] | Barr, M.; Wells, C., Toposes Triples and Theories (1985), Springer: Springer Berlin · Zbl 0567.18001 |

[2] | Bénabou, J., Introduction to bicategories, (Lecture Notes in Mathematics, 47 (1967), Springer: Springer Berlin), 1-77 · Zbl 1375.18001 |

[3] | S. Eilenberg and R.H. Street, manuscript in preparation.; S. Eilenberg and R.H. Street, manuscript in preparation. |

[4] | Johnson, M., Pasting diagrams in \(n\)-categories with applications to coherence theorems and categories of paths, (Doctoral Thesis (1987), University of Sydney) |

[5] | Johnson, M.; Walters, R. F.C., On the nerve of an \(n\)-category, Cahiers Topologie Géom. Différentielle, 28, 257-282 (1987) · Zbl 0662.18006 |

[6] | Kelly, G. M.; Street, R. H., Review of the elements of 2-categories, Lecture Notes in Mathematics, 420, 75-103 (1974) · Zbl 0334.18016 |

[7] | A.J. Power, A 2-category pasting theorem, J. Algebra, to appear.; A.J. Power, A 2-category pasting theorem, J. Algebra, to appear. · Zbl 0698.18005 |

[8] | Schanuel, S., Lecture to the Sydney Category Seminar (1988) |

[9] | Street, R. H., Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra, 8, 149-181 (1976) · Zbl 0335.18005 |

[10] | Street, R. H., The algebra of oriented simplexes, J. Pure Appl. Algebra, 49, 283-335 (1987) · Zbl 0661.18005 |

[11] | Street, R. H.; Walters, R. F.C., Yoneda structures on 2-categories, J. Algebra, 50, 350-379 (1978) · Zbl 0401.18004 |

[12] | Walters, R. F.C., A categorical approach to universal algebra, (Doctoral Thesis (1970), Australian National University) · Zbl 0211.32104 |

[13] | Walters, R. F.C., Lecture to the Sydney Category Seminar (1971) |

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