Theorems · Theorem · category theory

Action.preservesLimit_of_preserves

∀ {V : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} V] {G : Type u_2} [inst_1 : Monoid G] {C : Type u_3}
  [inst_2 : CategoryTheory.Category.{v_2, u_3} C] (F : CategoryTheory.Functor C (Action V G)) {J : Type u_4}
  [inst_3 : CategoryTheory.Category.{v_3, u_4} J] (K : CategoryTheory.Functor J C),
  CategoryTheory.Limits.PreservesLimit K (F.comp (Action.forget V G)) → CategoryTheory.Limits.PreservesLimit K F

F : C ⥤ Action V G preserves the limit of some K : J ⥤ C if it does after postcomposing with the forgetful functor Action V G ⥤ V.

Defined in

Mathlib.CategoryTheory.Action.Limits

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryMonoidCategoryTheory.CategoryCategoryTheory.Category