Timeline for Constructions unique up to non-unique isomorphism
Current License: CC BY-SA 2.5
5 events
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Jan 31, 2011 at 9:21 | comment | added | Harry Gindi | So when I said above "the functor $(-)\times S$", I was abusing language, since any given construction of "the" functor is only "a functor $(-)\times S$". This might seem like we're being overly cautious, but when we move from isomorphism of objects to equivalence of objects (in a bicategory), this makes some difference. This can be resolved by using Mac Lane's coherence theorem for bicategories, but, when we move up to tricategories, such a coherence theorem is proven not to exist. | |
Jan 31, 2011 at 9:16 | comment | added | Harry Gindi | @Andres: What David is referring to is the fact that universal constructions in category theory have this property, and that this is only a new feature of set theory. For instance, suppose we want to make the product with an object $S$ a functor (i.e. the functor $(-)\times S$. However, while the product is unique up to unique isomorphism, we have to choose a representative of each isomorphism class as well as the connecting morphisms between them. This requires choice or global choice, but after we choose a specific representative of the functor usign choice, it is unique up to unique iso. | |
Jan 31, 2011 at 0:47 | comment | added | Andrés E. Caicedo | Ok, @David, I'm curious. What do you mean? | |
Jan 30, 2011 at 20:47 | comment | added | David Roberts♦ | Sounds like a case for 'the': ncatlab.org/nlab/show/the | |
Jan 30, 2011 at 16:46 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |