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I fixed some of the references at Batanin omega-category.
Here is a question:
around corollary 9.4 of
it is shown for the special case of Gray-categories that the weak $\omega$-functors of
are actually the resolved morphisms with respect of a canonical model category structure, out of cofibrant resolutions into fibrant objects.
Is an analog of this known for general Batanin $\omega$-categories? Is there a canonical model structure on Batanin $\omega$-categories such that the weak $\omega$-functors represent the correct derived hom-space?
AFAIK that is not known.
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