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Jan 29, 2010 at 1:26 vote accept Rado
Jan 29, 2010 at 1:26 comment added Rado Thanks, for some reason I thought that there always was an explicit isomorphism (something along the frobenius map), but it was not clear (or proven) whether it is canonical. Although, it still seems the "functoriality" you mention above is (at least partially) captured by the nat.transformation definition if the functors are defined properly. In any case, I will try to digest CFT better first and then go back to the foundational questions.
Jan 28, 2010 at 11:37 comment added José Figueroa-O'Farrill Sure, but the "particular property" in Pete's answer goes into the definition of the comma category.
Jan 28, 2010 at 10:19 history edited Pete L. Clark CC BY-SA 2.5
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Jan 28, 2010 at 10:15 comment added Harry Gindi The unique isomorphisms from the initial and terminal object are actually unique, and all of the universality properties can be expressed by choosing appropriate initial and terminal objects in the various comma categories (not restricted to slice categories).
Jan 28, 2010 at 10:00 history edited Pete L. Clark CC BY-SA 2.5
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Jan 28, 2010 at 8:48 history answered Pete L. Clark CC BY-SA 2.5