Timeline for Is there a notation for natural isomorphism?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2010 at 7:46 | comment | added | S. Carnahan♦ | If you want to know what the isomorphism is, you could write something like $\overset{\simeq}{\underset{\phi}{\longrightarrow}}$. | |
| Nov 11, 2010 at 7:22 | answer | added | zorglub | timeline score: 2 | |
| Nov 11, 2010 at 5:21 | comment | added | David Roberts♦ | I agree with Scott - it is far better to say that two functors are isomorphic, than just to display an isomorphism and say it is natural. Because, what is it natural with respect to? There are some natural isomorphisms that are natural only with respect to arrows in a subcategory of the domain of the corresponding functor, and this is crucial information. | |
| Nov 11, 2010 at 5:03 | comment | added | BCnrd | Merely knowing two functors are naturally isomorphic is often inadequate: it is important to know what the isomorphism is (or perhaps its inverse), or at least how it can be uniquely characterized (so it can be used in many ways). | |
| Nov 11, 2010 at 4:05 | comment | added | S. Carnahan♦ | It's not clear this is necessary. One could write the appropriate functors, and then use $\cong$ to say that the functors are isomorphic. | |
| Nov 11, 2010 at 3:49 | history | asked | David Corwin | CC BY-SA 2.5 |