Timeline for General construction for internal hom in a presheaf category
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2010 at 22:38 | comment | added | Mike Shulman | You can spell out the definition of homs in presheaf categories in terms of an end in Set, if you like: $G^F(c) = Hom(y(c)\times F, G) = \int_{c'} Hom(C(c,c')\times F(c'), G(c'))$. You could then invoke the construction of limits in Set, so that $G^F(c)$ is the set of tuples $(h_{c'})_{c'\in C}$, where $h_{c'}\colon C(c,c')\times F(c')\to G(c')$, such that for any $\gamma\colon c'\to c''$ in $C$ we have $G(\gamma) \circ h_{c'} = h_{c''} \circ (C(c,\gamma) \times F(\gamma))$. | |
| Jan 1, 2010 at 22:28 | vote | accept | Harry Gindi | ||
| Jan 1, 2010 at 22:28 | comment | added | Harry Gindi | Accepted and +1, but is there any way to obtain a more concrete description? | |
| Jan 1, 2010 at 22:22 | history | answered | Mike Shulman | CC BY-SA 2.5 |