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.
Cigoli, A.S., Mantovani, S., Metere, G. (2023). On Pseudofunctors Sending Groups to 2-Groups. MEDITERRANEAN JOURNAL OF MATHEMATICS, 20(1) [10.1007/s00009-022-02220-1].
On Pseudofunctors Sending Groups to 2-Groups
Cigoli, AS;Metere, G
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. IfBis additive, this is the case precisely when the associated opfibration has groupoidal fibres.
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