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?

Cauchy characterization of enriched categories. $\endgroup$ – Mike Shulman Feb 24 '17 at 10:27pseudolimits do not exist, lax (and colax?) limits exist and coincide with colimits. This seems a pretty rigid structure, although I see why it is true. Street's paper, that I completely removed from my memory, seems to address part of my question in full generality. Have his work had some sequel? If yes, add it and I'll consider it an answer :-) $\endgroup$ – fosco Feb 24 '17 at 11:21