Timeline for Dual of $n$-cosheaf is an $n$-sheaf?
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| Sep 21, 2020 at 22:08 | comment | added | Tim Campion | I agree with Qiaochu, modulo the fact that your definition of an $n$-cosheaf is wrong. The right definition of a sheaf valued in an $\infty$-category $C$ says that for any cover $U_\bullet \to U$, we have that $\mathcal F(U)$ is canonically equivalent to the $\infty$-categorical limit of the functor $\Delta \to C$, $[n] \mapsto \prod_{i_0,\dots,i_n} \mathcal F(U_{i_0} \times_U \cdots \times_U U_{i_n})$. If $C$ is an $n+1$-category like $Cat_n$, then I believe you can truncate this simplicial object at level $n+1$ and still get things right. Cosheaves should be defined by the analogous colimit. | |
| Sep 21, 2020 at 19:16 | comment | added | Qiaochu Yuan | Yes, Homs send colimits to limits always. | |
| Sep 21, 2020 at 18:40 | history | asked | curious math guy | CC BY-SA 4.0 |