Timeline for On the coherence theorem for bicategories
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2015 at 13:56 | vote | accept | Espen Nielsen | ||
| Mar 2, 2015 at 14:43 | comment | added | Chris Schommer-Pries | the answer is again yes. See remark 3 at the end of Lack's paper which Todd mentions. | |
| Mar 2, 2015 at 14:41 | comment | added | Chris Schommer-Pries | However something like the above statement is true if you restrict the class of 2-categories even further. There is a class of "cofibrant" 2-categories which do have the property that every weak functor out of them is equivalent to a strict functor, and similarly for transformations. Most proofs of the coherence theorem actually show that every bicategory is equivalent to a cofibrant 2-category (for example the proof via Yonneda embedding does this, though not obviously). So is "2-cat" means cofibrant 2-categories, strict functors, strict transformations, and modifications then (cont) | |
| Mar 2, 2015 at 14:36 | comment | added | Chris Schommer-Pries | Just adding to Todd's answer, we the op writes "2-cat" it is ambiguous. The objects are certainly strict 2-cats, but what are the bicats of morphisms? If they are all weak functors, transformations, and modifications, then the answer to the op's question is "yes". However if what is meant is that we use strict functors and strict transformations (and modifications) then the answer is "no, these are not equivalent", as Lack shows. The key problem is that there can be weak functors between strict 2-categories which are not equivalent to strict functors between the same 2-categories. (cont) | |
| Mar 2, 2015 at 14:02 | history | answered | Todd Trimble | CC BY-SA 3.0 |