Timeline for Why should morphisms between two graded vector spaces preserve grading?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2012 at 6:40 | history | edited | tzhang | CC BY-SA 3.0 |
added 14 characters in body
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| Jul 11, 2012 at 21:56 | comment | added | Matthias Ludewig | If one defines the morphisms to include the "any h case", then one obtains a grading on HOM(V, W) that turns it into a graded algebra - so this should be quite natural! | |
| Jul 11, 2012 at 18:10 | answer | added | Peter May | timeline score: 9 | |
| Jul 11, 2012 at 13:02 | answer | added | Fred Rohrer | timeline score: 3 | |
| Jul 11, 2012 at 12:04 | answer | added | Kevin Walker | timeline score: 1 | |
| Jul 11, 2012 at 9:54 | comment | added | Fernando Muro | You can actually define morphisms as homomorphisms on the underlying vector space. The definition of morphisms should be motivated by the application you have in mind. There are different possible choices. | |
| Jul 11, 2012 at 7:45 | comment | added | Martin Brandenburg | tea.mathoverflow.net/discussion/1392/… | |
| Jul 11, 2012 at 5:04 | comment | added | Mark Grant | Your HOM consists of morphisms of degree $h$. If you compose two such I think you get something of degree $2h$, so this will not be a category. Or do you mean to let $h$ be any element of $H$ in the definition of HOM? | |
| Jul 11, 2012 at 5:03 | comment | added | Mariano Suárez-Álvarez | Well, this gives the wrong notion of isomorphism if it gives the wrong notion of isomorphism. It could well be the correct one—one needs a context to know! It is not like one does not see in nature categories with the same objects but different morphisms, after all... | |
| Jul 11, 2012 at 4:46 | comment | added | S. Carnahan♦ | I agree with Qiaochu. Your category is the Tannakian category $Rep(D(G))$. Here $D(G)$ is the diagonalizable group scheme $\underline{Hom}(G, \mathbb{G}_m)$ (see SGA3). | |
| Jul 11, 2012 at 4:00 | history | edited | MTS | CC BY-SA 3.0 |
Fixed some latex
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| Jul 11, 2012 at 2:57 | comment | added | Qiaochu Yuan | It gives the wrong notion of isomorphism. Of course the internal hom is useful, but as an internal hom. | |
| Jul 11, 2012 at 2:55 | history | asked | tzhang | CC BY-SA 3.0 |