Timeline for What's after natural transformations?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2010 at 6:55 | comment | added | Mike Shulman | "n-transformation" is already used to mean a natural transformation (= 1-transfor) between functors between n-categories, just as "n-functor" means a functor between n-categories. I prefer to drop both prefixes when possible, but I think reusing the same prefixes with a different meaning invites confusion. "Transfor" is due to Sjoerd Crans and is a portmanteau of "transformation" and "functor." One can think of a k-transfor as like a degree-k map of chain complexes: it takes each 0-cell to a k-cell, each 1-cell to a (k+1)-cell, etc. -- this unifies functors with higher transfors. | |
| Jul 27, 2010 at 12:18 | comment | added | Urs Schreiber | n-transfor(mation)s are in fact a lot like functors: they are functors C x G^n --> D for G^n is the n-category free on the cellular n-globe. | |
| Jul 23, 2010 at 15:54 | comment | added | Michael A Warren | If you work with n-categories enough you start to realize that natural transformation and modifications of n-categories are really a different sort of thing than functors (which makes Scott's suggestion less attractive). But I'd have thought that "n-transformation" is a bit more attractive than "n-transfor" (and, indeed, "n-transformation" is what I've always used for this purpose). | |
| Jul 21, 2010 at 19:17 | comment | added | Urs Schreiber | One could also say that an n-transfor is a directed homotopy of order n in the ambient whatever category of whatever categories. Cause in the case where all n-categories here are in fact n-groupoids / infty-groupoids, an n-transfor is nothing but an order n homotopy (under the identification of oo-groupoids with topological spaces). | |
| Jul 21, 2010 at 19:15 | comment | added | Urs Schreiber | Scott, the term n-functor is already widely established to mean a morphism between n-categories. | |
| Jul 21, 2010 at 19:14 | history | edited | Urs Schreiber | CC BY-SA 2.5 |
added 22 characters in body
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| Jul 21, 2010 at 17:02 | comment | added | Simon Rose | This sort of reminds me of the naming of higher derivatives of position. We have velocity and acceleration which are common, then after that there are the increasingly obscure 'jerk' for the third derivative, and then 'snap', 'crackle', and 'pop' for the fourth, fifth, and sixth derivatives. | |
| Jul 21, 2010 at 16:59 | comment | added | Kim Morrison | I prefer to rearrange the terminology, and just have plain functors between n-categories, 2-functors between functors (so, in the n=1 case, 2-functors are the same as natural transformations), 3-functors between 2-functors, and so on. | |
| Jul 21, 2010 at 15:36 | comment | added | Mariano Suárez-Álvarez | Urgh. Is transfor an established term? :( | |
| Jul 21, 2010 at 15:28 | history | answered | Urs Schreiber | CC BY-SA 2.5 |