Timeline for What does an object of isomorphisms look like?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2013 at 23:55 | vote | accept | ct-novice | ||
| Sep 10, 2013 at 23:55 | comment | added | ct-novice | I'm primarily interested in categories for their connection to denotational semantics of lambda calculi. My question is motivated by wondering what the type of "type equivalences" is. We might consider types (objects of a category) equal if there is an iso between them, or we might be interested in the stronger property that there is a unique iso (I'm not sure). In the latter case, I suppose the classifying object would either be (isomorphic to) the terminal object or the initial object; but which it is depends on $A$ and $B$. | |
| Sep 9, 2013 at 9:03 | comment | added | Colin McLarty | If there is exactly one isomorphism from $A$ to $B$ (or indeed if there is exactly one of anything, in a category with terminal object) then that isomorphism (or whatever) is classified by the terminal object. You probably have some other idea hidden behind this one of unique isomorphisms. | |
| Sep 9, 2013 at 3:46 | review | First posts | |||
| Sep 9, 2013 at 4:14 | |||||
| Sep 9, 2013 at 3:41 | comment | added | ct-novice | Suppose $\phi$ is an iso from $A$ to $B$. Then $\phi$ is unique if, for every other iso $\phi'$ from $A$ to $B$, $\phi = \phi'$. | |
| Sep 9, 2013 at 3:35 | answer | added | Qiaochu Yuan | timeline score: 11 | |
| Sep 9, 2013 at 3:31 | comment | added | Mariano Suárez-Álvarez | What are the "unique isomorphisms" from $A$ to $B$? | |
| Sep 9, 2013 at 3:28 | history | asked | ct-novice | CC BY-SA 3.0 |