More on strictification

Another fascinating day! At lunch time Steve Lack told me some interesting things about the strictification operator for bicategories. Apparently section 5.6 of [GPS] is wrong, and Steve reckons Gray is probably not triequivalent to Bicat. (The mistake in 5.6 is in the very first sentence: the trihomomorphism M: B → Gray constructed there is not actually a triequivalence! Although it’s locally a biequivalence by construction, it fails to be triessentially surjective.)

On the other hand, Steve mentioned a sense in which strictification does produce a (Quillen) equivalence: see his paper here. Perhaps this is my cue to finally learn about model categories…

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