Timeline for Is there a tricategory of bicategories and biprofunctors?
Current License: CC BY-SA 2.5
3 events
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| Sep 3, 2010 at 7:11 | comment | added | Mike Shulman | Do you need "your" profunctors to compose in a "coend" type way? Would it be enough to show that functors $C\times D^{op}\to Cat$ are equivalent to cocontinuous functors $Cat^{C^{op}} \to Cat^{D^{op}}$, and then use composition of the latter functors to induce a composition operation on the former? | |
| Aug 27, 2010 at 22:06 | comment | added | Evan Jenkins | Unfortunately, I really do need profunctors in the sense of maps $\mathcal{C} \times \mathcal{D}^{\operatorname{op}} \to \operatorname{Cat}$. As you say, if we could show that "my" profunctors are the same as "your" profunctors (bicolimit-preserving bifunctors between bipresheaf categories), we'd be done. The $(\infty, 1)$-categorical version would be sufficient for my purposes, but I do not believe anybody has yet worked out how to compose "my" profunctors in this setting (although I know that there are people actively thinking about these things). | |
| Aug 27, 2010 at 12:45 | history | answered | Urs Schreiber | CC BY-SA 2.5 |