## The Eckmann-Hilton argument, higher operads and En-spaces, available at http://www.ics.mq.edu.au

Venue: | mbatanin/papers.html of Homotopy and Related Structures |

Citations: | 32 - 5 self |

### BibTeX

@INPROCEEDINGS{Batanin_theeckmann-hilton,

author = {M. A. Batanin},

title = {The Eckmann-Hilton argument, higher operads and En-spaces, available at http://www.ics.mq.edu.au},

booktitle = {mbatanin/papers.html of Homotopy and Related Structures},

year = {},

pages = {37}

}

### Years of Citing Articles

### OpenURL

### Abstract

The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the commutativity of the higher homotopy groups. A reformulation of this argument in the language of higher categories is: suppose we have a one object, one arrow 2-category, then its Hom-set is a commutative monoid. A similar argument due to A.Joyal and R.Street shows that a one object, one arrow tricategory is ‘the same’ as a braided monoidal category. In this paper we extend this argument to arbitrary dimension. We demonstrate that for an n-operad A in the author’s sense there exists a symmetric operad S n (A) called the n-fold suspension of A such that the