Dear Ross,
If V = 2Cat then V-Cat = 3Cat . . . and on it goes.
OK. So if V = omegaCat, then V-Cat = omegaCat. Now how do you define (recursively) the internal-hom of omegaCat? David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[From moderator: apologies to Tom, sent previously with bad header] Dear David, You asked about recursive definitions of the category of (strict) omega-categories.
OK. So if V = omegaCat, then V-Cat = omegaCat.
More than that: omegaCat is the terminal coalgebra for the endofunctor V |--> V-Cat of the category of locally small categories with finite products. This can be regarded as a (co)recursive definition of omegaCat. As far as I know, this was first observed by Carlos Simpson. Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Tom,
This can be regarded as a (co)recursive definition of omegaCat.
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?
As far as I know, this was first observed by Carlos Simpson.
Any reference? David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear David, You asked about recursive definitions of the category of (strict) omega-categories.
OK. So if V = omegaCat, then V-Cat = omegaCat.
More than that: omegaCat is the terminal coalgebra for the endofunctor V |--> V-Cat of the category of locally small categories with finite products. This can be regarded as a (co)recursive definition of omegaCat. As far as I know, this was first observed by Carlos Simpson. Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
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David Leduc -
majordomo＠mlist.mta.ca -
Tom Leinster