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. If B is additive, this is the case precisely when the associated opfibration has groupoidal fibres.
On Pseudofunctors Sending Groups to 2-Groups
Cigoli A. S.;
2023-01-01
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. If B is additive, this is the case precisely when the associated opfibration has groupoidal fibres.
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