Talk:Category of functors
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C^{op}} 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.