Talk:Category of functors: Difference between revisions
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imported>Giovanni Antonio DiMatteo (New page: 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 represent...) |
imported>Aleksander Stos m (subpages) |
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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 <math>C^{op}</math> 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 <math>\eta_U</math> would go from F to G with dashed lines or something. I dunno, I think it could be visually helpful. | 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 <math>C^{op}</math> 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 <math>\eta_U</math> would go from F to G with dashed lines or something. I dunno, I think it could be visually helpful. | ||
Latest revision as of 01:45, 15 January 2008
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.
