Timeline for Is there any nontrivial monad on the category of graphs?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2020 at 18:50 | comment | added | Tomáš Jakl | The second example that Andrej wrote arises from the adjunction between $\prod$ and $\Delta$ in ncatlab.org/nlab/show/category+of+simple+graphs | |
| Apr 28, 2013 at 13:53 | comment | added | Andrej Bauer | I think this proves I am very smart. Had I been doing things randomly, at least some of these would be actual examples. It takes a special talent to produce four plausibly-sounding non-examples. | |
| Apr 28, 2013 at 3:25 | comment | added | Peter LeFanu Lumsdaine | In the currently last example, sending $G$ to the discrete graph on $\pi_0(G)$, isn’t there a problem with the unit morphism — edges within each connected component have no edges to map to? | |
| Apr 19, 2013 at 21:49 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
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| Apr 19, 2013 at 6:43 | comment | added | Gejza Jenča | Please, do not delete the answer. The last example is correct,I think. | |
| Apr 19, 2013 at 6:08 | comment | added | Gejza Jenča | The third example is not a functor, I think: take the path with 3 vertices $P_3$. It can be 2-colored, so there is a morphism into $K_2$. But there is no morphism $K_3\to K_2$. | |
| Apr 18, 2013 at 22:12 | comment | added | Andrej Bauer | But surely, there are billions and billions of them. | |
| Apr 18, 2013 at 22:11 | comment | added | Andrej Bauer | Ugh, maybe I should just delete the answer. | |
| Apr 18, 2013 at 13:34 | comment | added | Todd Trimble | I'm not sure the complete graph example works. If you apply such a completion functor to the function $2 \to 1$ from the 2-element set to the 1-element set (with the discrete graph structures), where would the edge in the completion of $2$ go to? | |
| Apr 18, 2013 at 13:26 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
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| Apr 18, 2013 at 13:25 | comment | added | Andrej Bauer | Oops, that would be a comonad then. Thanks! | |
| Apr 18, 2013 at 12:41 | comment | added | Andreas Blass | In the second example, the discrete graph on the same vertices, what is the unit of the monad? | |
| Apr 18, 2013 at 12:34 | history | answered | Andrej Bauer | CC BY-SA 3.0 |