Commit 2024-10-23 02:43 c48f8a2c
View on Github →feat(CategoryTheory/Adjunction): the left partial adjoint (#17388)
Given a functor F : D ⥤ C
, we define a functorF.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ D
which is defined on a certain full subcategory of C
. It satisfies similar properties to the left adjoint of F
(if this existed). We show that the domain of definition of this partial left adjoint is stable under certain colimits.
This shall be used in #17366 in order to show the existence of the pullback functor on categories of presheaves of modules.