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}
[CategoryTheory.Category.{u_5, u_1} A]
[CategoryTheory.Category.{u_6, u_2} C]
[CategoryTheory.Category.{u_4, u_3} J]
[CategoryTheory.Limits.HasColimitsOfShape J A]
[CategoryTheory.HasExactColimitsOfShape J A]
[CategoryTheory.Limits.HasFiniteLimits A]
:
instance
CategoryTheory.instHasExactLimitsOfShapeFunctorOfHasFiniteColimits
{A : Type u_1}
{C : Type u_2}
{J : Type u_3}
[CategoryTheory.Category.{u_5, u_1} A]
[CategoryTheory.Category.{u_6, u_2} C]
[CategoryTheory.Category.{u_4, u_3} J]
[CategoryTheory.Limits.HasLimitsOfShape J A]
[CategoryTheory.HasExactLimitsOfShape J A]
[CategoryTheory.Limits.HasFiniteColimits A]
: