Talk:Category of functors

From Citizendium
Revision as of 01:45, 15 January 2008 by imported>Aleksander Stos (subpages)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
This article is developing and not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
To learn how to update the categories for this article, see here. To update categories, edit the metadata template.
 Definition Category whose objects are functors in another category and whose morphisms are natural transformations. [d] [e]
Checklist and Archives
 Workgroup category Mathematics [Categories OK]
 Talk Archive none  English language variant American English

It would be cool if someone could make a nice computer drawing like as follows, to explain the idea of natural transformation: you have a big circle in the lower left, it vaguely represents the category somehow... and a big circly in the upper right representing D somehow... to "know" a functor is to know what it does to arrows, so fix an arrow f in C (draw it) then in D you have two arrows... F(f) and G(f)... so a natural transformation should be comparing these two arrows... i.e., we'd need morphisms making the square commute. (so those would go from F to G with dashed lines or something. I dunno, I think it could be visually helpful.