Bryce Clark

Date: March 26, 2021

Time: 4:00 PM MDT

Location: Zoom (email benjamin dot macadam for details)

Title: The Grothendieck construction for lenses

Abstract: The Grothendieck construction, which describes an equivalence between functors into Cat and split 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. Delta lenses are a generalisation of split opfibrations, where the chosen lifts need not be opcartesian. The purpose of this talk is to investigate the question: is there also some kind of generalised Grothendieck construction which yields delta lenses? The main result establishes 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. We will also see how several examples of delta lenses, including split opfibrations, may be understood from this perspective.