Timeline for When do we study maps into an object or from the object to another object?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2010 at 14:52 | comment | added | Pete L. Clark | @David: Thanks for the link; it looks interesting. (I am not surprised that the orientation question has been asked before...) | |
| Nov 28, 2010 at 13:34 | comment | added | David Corfield | Orientation of categories has cropped up at the n-Category Cafe, e.g., golem.ph.utexas.edu/category/2009/06/kan_lifts.html#c024719, golem.ph.utexas.edu/category/2009/05/…, and golem.ph.utexas.edu/category/2008/12/…. | |
| Nov 28, 2010 at 5:42 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Nov 28, 2010 at 0:28 | comment | added | Qiaochu Yuan | @Martin: at least for the category of affine schemes I think the answer is "it behaves more like Set than the opposite category." | |
| Nov 27, 2010 at 22:58 | comment | added | Martin Brandenburg | "Why do most categories come with a "natural orientation"" is a very nice interpretation of the question! | |
| Nov 27, 2010 at 20:35 | comment | added | Bruno Stonek | @Pete: agreed. I would like to especially recommend this paper: maths.gla.ac.uk/~tl/categories/yoneda.ps . I quote the last page: "two objects look the same if and only if they look the same from all viewpoints". This is formally explored in that paper, and in full generality, I believe. | |
| Nov 27, 2010 at 19:36 | comment | added | Brian | Thanks for your answer. This is exactly the question I am asking: when we write $X = \mathrm{Spec} A$, already implicitly, we are viewing $A$ as the ring of functions from $X$ to $\mathrm{Spec} K[x]$. | |
| Nov 27, 2010 at 19:31 | comment | added | Pete L. Clark | P.S.: If one is going to mention categories at all, I suppose "Yoneda Lemma" should occur in the answer somewhere. But there are others who enjoy talking about this material more than I... | |
| Nov 27, 2010 at 19:29 | history | answered | Pete L. Clark | CC BY-SA 2.5 |