[Merged by Bors] - feat: the forget functor from commutative groups to groups preserves all limits #11669
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…all limits (#11669) It is shown in this PR that the forget functor from commutative groups to groups preserves all limits (regardless of the universe parameters of the index category). It is also shown that a functor `F : J ⥤ CommGroupCat` (or `F : J ⥤ GroupCat`) has a limit iff the type `(F ⋙ forget _).sections` is small. This is related to the fact that the forget functor `CommGroupCat.{u} ⥤ Type u` is corepresentable (by `ULift ℤ`). Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
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…all limits (#11669) It is shown in this PR that the forget functor from commutative groups to groups preserves all limits (regardless of the universe parameters of the index category). It is also shown that a functor `F : J ⥤ CommGroupCat` (or `F : J ⥤ GroupCat`) has a limit iff the type `(F ⋙ forget _).sections` is small. This is related to the fact that the forget functor `CommGroupCat.{u} ⥤ Type u` is corepresentable (by `ULift ℤ`). Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
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…all limits (#11669) It is shown in this PR that the forget functor from commutative groups to groups preserves all limits (regardless of the universe parameters of the index category). It is also shown that a functor `F : J ⥤ CommGroupCat` (or `F : J ⥤ GroupCat`) has a limit iff the type `(F ⋙ forget _).sections` is small. This is related to the fact that the forget functor `CommGroupCat.{u} ⥤ Type u` is corepresentable (by `ULift ℤ`). Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
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It is shown in this PR that the forget functor from commutative groups to groups preserves all limits (regardless of the universe parameters of the index category). It is also shown that a functor
F : J ⥤ CommGroupCat(orF : J ⥤ GroupCat) has a limit iff the type(F ⋙ forget _).sectionsis small. This is related to the fact that the forget functorCommGroupCat.{u} ⥤ Type uis corepresentable (byULift ℤ).