Timeline for "Canonical" graph structure on $\text{Hom}(G, H)$
Current License: CC BY-SA 3.0
4 events
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| Jul 10, 2015 at 13:33 | comment | added | Eric Wofsey | No, the counterexample coming from the adjoint of a projection still rules that out. By the way, if there were an exponential object (as there is in the category of graphs with loops), its vertex set would not be $\operatorname{Hom}(G,H)$, but the set of all maps from $V(G)$ to $V(H)$ (since $\bullet\times G$ is $G$ with all its edges removed). The graph-homomorphisms would just be those vertices of the exponential object that have loops. This reflects the fact that (in the category of graphs with loops) the terminal object is a vertex with a loop, not just a vertex. | |
| Jul 10, 2015 at 12:07 | comment | added | Dominic van der Zypen | Is there a construction that's adjoint to the categorical product? | |
| Jul 10, 2015 at 6:38 | vote | accept | Dominic van der Zypen | ||
| Jul 9, 2015 at 23:32 | history | answered | Eric Wofsey | CC BY-SA 3.0 |