Timeline for Left adjoints for functors out of a Deligne-Kelly tensor product
Current License: CC BY-SA 4.0
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| Apr 24, 2022 at 10:32 | comment | added | Adrien | I think the condition you're asking for implies instead that $T$ has a colimit preserving right adjoint. If $H$ is an Hopf algebra, then the category of $H$-modules does not satisfy your conditions, yet the tensor product has a left adjoint (induction along the coproduct). On the other hand, the category of $H$-comodules does satisfy your assumption, but then (I'm not entirely sure) I think the tensor product won't have a left adjoint in general | |
| Apr 24, 2022 at 8:45 | history | asked | Thibault Décoppet | CC BY-SA 4.0 |