Lax double functors into Span-like double categories
Bryce Clarke – 30 September 2020
The category of elements construction, which describes an equivalence between functors into Set and discrete opfibrations, may be generalised in several ways. One such generalisation is the equivalence between lax double functors into Span, from a small category B, and ordinary functors into B. In the paper "Lax Presheaves and Exponentiability", Niefield studies the cases when spans are replaced with relations (jointly-monic spans) or partial functions (spans with monic left leg). The purpose of this talk is to examine the case when spans are replaced with multi-valued functions (spans with epic left leg). The main result will prove an equivalence between lax double functors from a small category B into sMult (the double category of "split" multi-valued functions) and delta lenses into B.