Timeline for 2-morphisms in structured 2-categories
Current License: CC BY-SA 2.5
3 events
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| Feb 7, 2011 at 18:24 | comment | added | Theo Johnson-Freyd | Hrm. No, I disagree. In part, I disagree because I don't think "the colimit" is as well-defined as your comment implies (although I think you'll agree with me). Namely, a colimit of a diagram is any initial cocone over the diagram. So when I say that a functor "preserves colimits", what I'm saying is that any colimit cocone you feed into it comes out as some colimit cocone. In particular, I disagree that the comparison isomorphism should need to exist. | |
| Feb 7, 2011 at 6:04 | comment | added | Mike Shulman | I'm not sure I agree entirely with your description of the second example. A colimit-preserving functor has a 2-morphism as well: the comparison isomorphism between the image of the colimit and the colimit of the image. It just so happens that that isomorphism is uniquely determined if it exists. | |
| Feb 6, 2011 at 20:29 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |