Str-omega-cat is cartesian-closed?

Str-omega-cat is cartesian-closed?

[Harry Gindi]

Dear All,

According to Sjoerd Crans's thesis, specifically Chapter III, section 10.2, the composition
operations defined on [A,B] in Ross Street's paper,  "The algebra of oriented simplices",
do not give [A,B] the structure of a strict omega-category.

(Recall that [A,B] is taken to be the globular set defined by the formula:

[A,B]_n=Hom(D_n x A,B),

where D_n is the n-disk (or n-globe if it tickles your fancy)).

I can't exactly tell whether he (Crans) means to say that Str-omega-cat is not cartesian-closed,
or just simply that the proof was not correct but could be fixed with some amount of effort.

Is there a correct proof of this fact somewhere in the literature, and if not, would I be taking
a huge risk by neglecting to give a proof?

Thanks for the help!

Yours in friendship,

Harry Gindi


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