Dear David, Regarding omegaCat as the terminal coalgebra for ( )-Cat: On Mon, 27 Sep 2010, David Leduc wrote:
Good, good! I am thrilled by such (co)recursive definitions. In fact was asking about a (co)recursive of the cartesian closed structure of omegaCat. Do you have something in store?
I'm not aware that anyone has thought particularly about the cartesian closed structure in this context. But being cartesian closed is a *property*, not extra *structure*, and for reasons that Ross explained, it just comes along for the ride.
As far as I know, this was first observed by Carlos Simpson.
Any reference?
Simpson didn't write it up. However, Eugenia Cheng and I have some related theorems about non-strict omega-categories, which we're currently writing up, and our paper will include an account of Simpson's result. You can read some talk slides on this: see the very bottom of http://cheng.staff.shef.ac.uk/research.html Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
But being cartesian closed is a *property*, not extra *structure*,
"being cartesian closed is a property" but [_._] is structure, isn't it? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On Tue, Sep 28, 2010 at 9:11 AM, David Leduc <david.leduc6@googlemail.com>wrote:
But being cartesian closed is a *property*, not extra *structure*,
"being cartesian closed is a property" but [_._] is structure, isn't it?
I'm not sure what [_._] is supposed to mean - an internal hom functor? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I'm not sure what [_._] is supposed to mean - an internal hom functor?
This was supposed to be the "cartesian closed structure" of StrictOmegaCat, but since some say it is not a structure I'm not sure how to call it... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
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David Leduc -
John Baez -
Tom Leinster