Timeline for Is this a functor on the category of $C^{*}$ algebras?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2015 at 19:54 | vote | accept | Ali Taghavi | ||
| Oct 1, 2015 at 0:49 | comment | added | user13113 | Centers tend fit into category theory in a different way, as being the natural automorphisms of identity functors. (e.g. for a ring $R$, view it as a preadditive category with one object. Or view it as $R$-Mod) | |
| Sep 30, 2015 at 22:03 | answer | added | Yemon Choi | timeline score: 10 | |
| Sep 30, 2015 at 21:25 | comment | added | Yemon Choi | Just as general background information: it is a standard exercise in various introductions to category theory, to show that there is no functor on the category of groups which sends each group to its centre. If one knows this, then one would guess that the answer to your question is negative, as indeed seems to be the case | |
| Sep 30, 2015 at 15:55 | comment | added | Igor Khavkine | Algebra homomorphisms don't always send centers to centers, so the obvious idea of defining $Z(\alpha\colon A \to B)$ to be the restriction of $\alpha$ to $A(Z)$ doesn't work. | |
| Sep 30, 2015 at 15:54 | answer | added | Simon Henry | timeline score: 10 | |
| Sep 30, 2015 at 15:32 | history | asked | Ali Taghavi | CC BY-SA 3.0 |