## The importance of omega-operad of coendomorphism in Higher Category Theory

### Camell Kachour – 29 August 2012, 5 September 2012

Two years ago I have pointed out the importance of omega-operad of coendomorphism to describe the weak omega category of the weak omega categories, up to a "contractibility hypothesis". In fact this technology of omega-operads of coendomorphism can be adapted for many higher structures, without any hypotheses : For instance we are going to describe the omega-graph of the omega-graphs, the reflexive omega-graphs of the reflexive omega-graphs, the omega-magma of the omega-magmas, and the reflexive omega-magma of the reflexive omega-magmas, all that by using the same technology, where omega-operads of coendomorphism play a central role.

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