I learned that the bicategory $\bf Prof$, while having lots of interesting properties, does not admit inverters, so it does not admit arbitrary pseudolimits.
Does this imply that it is impossible to define some useful constructions, like comma objects?
More in general, is there a precise account of which co/limits, bi-co/limits, and weighted co/limits can be constructed in $\bf Prof$?
In fact, in the thread above I say that $\bf Prof$ admits $\bf Cat$-cotensors, and I'm quite sure that ${\cal A}\pitchfork \bf B$ is defined on objects by $({\cal A},{\bf B})\mapsto {\bf A}^°\otimes {\bf B}$ (boldface = 1-cells of $\bf Prof$; mathcal = 1-cells of $\bf Cat$); but I'm not able to see what how to build the canonical span $d_0,d_1 \colon {\cal I}\pitchfork {\bf B} \rightsquigarrow \bf B$ in the case ${\cal I}=\{0\to 1\}$: how is it possible to define two functors ${\cal B}\otimes{\cal I}^°\otimes {\cal B}^° \to {\cal V}$ that satisfy a similar property of evaluation on co/domain?