This is a continuation of my previous question.

A) Morphisms in (1') are basically internal anafunctors, their compositions heavily use (and only) pullback/limit.

B) Bibundles in (2) are basically special kind internal profunctores, their compositions heavily use quotient/coend/colimit.

We know that (1') and (2) are equivalent, this is a bit surprising since limit and colimit are usually very different notions. My question is which categorical properties make this true? Thanks.