Strictification avoids Choice?

Strictification avoids Choice?

[David Roberts]

Dear all,

reading Mac Lane and Pare's JPAA paper on coherence for bicategories,
it seems to me that both the strictification st(B) of a bicategory B
and the (weak) 2-functors st(B) --> B and B --> st(B) don't require
the axiom of choice (my copy of CWM is on loan, else I would check
more of the details -- for monoidal categories -- given there).

Is this true? Or rather, can we prove B <--> st(B) is an equivalence
of bicategories in the sense of having an adjoint biequivalence of
bicategories in the absence of choice? Is there a reference I can
point to, not of this statement, but of a result that justifies this?
Mac Lane and Pare do not seem to go far enough for me to reasonably
conclude this stronger statement.

Best regards,

David

PS the paper mentions that the coherence theorem for bicategories is a
special case of a result from Bénabou's thesis. I had a skim, but it
didn't leap out at me, and so apologies if everything I need is in
there and I couldn't see it.


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