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The results of this thesis allows one to replace calculations intricategories with equivalent calculations in Gray categories (aka semistricttricategories). In particular the rewriting calculus for Gray categories asused for example by the online proof assistant globular (arXiv:1612.01093), orequivalently the Gray-diagrams of arXiv:1211.0529 can then be used also in thecase of a fully weak tricategory.

The tricategory of formal composites and its strictification