Given a category $\mathcal{C}$, it follows from Proposition 4.1 of Day's

> *Brian Day*, _Limit spaces and closed span categories_, Lecture Notes in Mathematics, 420, 1974 ([doi:10.1007/BFb0063100](https://doi.org/10.1007/BFb0063100)).

That the bicategory $\mathsf{Span}_\mathcal{C}$ of spans in $\mathcal{C}$ has right Kan extensions and right Kan lifts iff $\mathcal{C}$ is locally Cartesian closed.

1. Does $\mathsf{Span}_\mathcal{C}$ also have left Kan extensions and left Kan lifts if (and perhaps only if?) $\mathcal{C}$ is locally Cartesian closed too?
2. What would be explicit descriptions for $\mathrm{Ran}$ and $\mathrm{Rift}$ in $\mathsf{Span}_{\mathcal{C}}$? What about for $\mathrm{Lan}$ and $\mathrm{Lift}$ if these also exist?