Timeline for Does every functor between Grothendieck categories have adjoints?
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| Aug 6, 2019 at 17:04 | comment | added | Simone Virili | Notice that, in Abelian categories, finite products and finite coproducts are the same; furthermore, a functor is additive if and only if it preserves finite coproducts. Hence, any functor between two Grothendieck categories that commutes either with limits or with colimits is necessarily additive. Hence, for a functor between Grothendieck categories to have any hope to be a (left or right) adjoint, it has to be additive. As a consequence: additivity here is not an hypothesis you have to add, it follows naturally by the rest of hypotheses. | |
| Aug 6, 2019 at 12:22 | answer | added | Todd Trimble | timeline score: 5 | |
| Aug 6, 2019 at 9:32 | history | asked | Operadbeginner | CC BY-SA 4.0 |