The category of type-valued sheaves is a regular epi category #
This file proves that when the target category D is a regular epi category (i.e. every epimorphism
is regular) and has pushouts and kernel pairs of epimorphisms, the functor category C ⥤ D is a
regular epi category. This is an instance that applies directly when D is Type*.
instance
CategoryTheory.Functor.instIsRegularEpiCategoryOfForallEpiHasPullbackOfHasPushouts
{C : Type u_1}
{D : Type u_2}
[Category.{u_4, u_1} C]
[Category.{u_3, u_2} D]
[∀ {F G : D} (f : F ⟶ G) [Epi f], Limits.HasPullback f f]
[Limits.HasPushouts D]
[IsRegularEpiCategory D]
:
IsRegularEpiCategory (Functor C D)