Hi, Given two strict omega-categories C and D, how do you define the strict omega-category of omega-functors between C and D? Thanks, David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Given two strict omega-categories C and D, how do you define the strict omega-category of omega-functors between C and D?
There is the Crans-Gray tensor product on StrOmegaCat that makes it biclosed monoidal. So for G^n the standard n-globe regarded as a strict omega-category, the (right/left) internal hom between strict omega-categories X and Y is [X,Y ] = Hom( X otimes G^bullet , Y ) . See http://ncatlab.org/nlab/show/Crans-Gray+tensor+product for references. Best, Urs [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Urs On 25/09/2010, at 1:13 AM, Urs Schreiber wrote:
Given two strict omega-categories C and D, how do you define the strict omega-category of omega-functors between C and D?
There is the Crans-Gray tensor product on StrOmegaCat that makes it biclosed monoidal.
I think David was asking about the simpler cartesian closed structure on omega-Cat. This is constructed in The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283-335 for example. Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
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David Leduc -
Ross Street -
Urs Schreiber