AB axioms in functor categories #
This file proves that, when the relevant limits and colimits exist, exactness of limits and
colimits carries over from A
to the functor category C тед A
instance
CategoryTheory.instHasExactColimitsOfShapeFunctorOfHasFiniteLimits
{A : Type u_1}
{C : Type u_2}
{J : Type u_3}
[Category.{u_5, u_1} A]
[Category.{u_6, u_2} C]
[Category.{u_4, u_3} J]
[Limits.HasColimitsOfShape J A]
[HasExactColimitsOfShape J A]
[Limits.HasFiniteLimits A]
:
HasExactColimitsOfShape J (Functor C A)
instance
CategoryTheory.instHasExactLimitsOfShapeFunctorOfHasFiniteColimits
{A : Type u_1}
{C : Type u_2}
{J : Type u_3}
[Category.{u_5, u_1} A]
[Category.{u_6, u_2} C]
[Category.{u_4, u_3} J]
[Limits.HasLimitsOfShape J A]
[HasExactLimitsOfShape J A]
[Limits.HasFiniteColimits A]
:
HasExactLimitsOfShape J (Functor C A)