On Pseudofunctors Sending Groups to 2-Groups

Abstract

For a category B with finite products, we first characterize pseudofunctors from B to Cat whose associated opfibration is Cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups to 2-groups. IfBis additive, this is the case precisely when the associated opfibration has groupoidal fibres.